{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 由于这部分代码在Sklearn中没有相关库，目前参考的[博客](http://blog.csdn.net/u010454729/article/details/49078505)\n",
    "[参考1](https://www.cnblogs.com/90zeng/p/apriori.html)\n",
    "\n",
    "[参考2](https://blog.csdn.net/wenyusuran/article/details/40736141)\n",
    "\n",
    "[参考3](https://blog.csdn.net/u010454729/article/details/49078505?spm=a2c4e.11153940.blogcont70455.16.19bc5bfdBuH32L)\n",
    "\n",
    "[扩展](https://www.cnblogs.com/lsqin/p/9342926.html)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### [代码解析](https://www.cnblogs.com/90zeng/p/apriori.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "code_folding": [],
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# 示例数据\n",
    "def loadDataSet():\n",
    "    return [[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]]\n",
    "# 创建每个项集元素长度为一的 \n",
    "def createC1(dataSet):\n",
    "    C1 = []\n",
    "    for transaction in dataSet:\n",
    "        for item in transaction:\n",
    "            if not [item] in C1:\n",
    "                C1.append([item])\n",
    "                \n",
    "    C1.sort()\n",
    "    return list(map(frozenset, C1))#use frozen set so we\n",
    "                            #can use it as a key in a dict    \n",
    "\n",
    "def scanD(D, Ck, minSupport):\n",
    "    ssCnt = {}\n",
    "    for tid in D:\n",
    "        for can in Ck:\n",
    "            if can.issubset(tid):\n",
    "                if can not in ssCnt: \n",
    "                    ssCnt[can]=1\n",
    "                else: ssCnt[can] += 1\n",
    "    numItems = float(len(list(D)))\n",
    "    retList = []\n",
    "    supportData = {}\n",
    "    for key in ssCnt:\n",
    "        support = ssCnt[key]/numItems\n",
    "        if support >= minSupport:\n",
    "            retList.insert(0,key)\n",
    "        supportData[key] = support\n",
    "    return retList, supportData\n",
    "\n",
    "def aprioriGen(Lk, k): #creates Ck\n",
    "    retList = []\n",
    "    lenLk = len(Lk)\n",
    "    for i in range(lenLk):\n",
    "        for j in range(i+1, lenLk): \n",
    "            L1 = list(Lk[i])[:k-2]; L2 = list(Lk[j])[:k-2]\n",
    "            L1.sort(); L2.sort()\n",
    "            if L1==L2: #if first k-2 elements are equal\n",
    "                retList.append(Lk[i] | Lk[j]) #set union\n",
    "    return retList\n",
    "\n",
    "def apriori(dataSet, minSupport = 0.5):\n",
    "    C1 = createC1(dataSet)\n",
    "    D = list(map(set, dataSet))\n",
    "    L1, supportData = scanD(D, C1, minSupport)\n",
    "    L = [L1]\n",
    "    k = 2\n",
    "    while (len(L[k-2]) > 0):\n",
    "        Ck = aprioriGen(L[k-2], k)\n",
    "        Lk, supK = scanD(D, Ck, minSupport)#scan DB to get Lk\n",
    "        supportData.update(supK)\n",
    "        L.append(Lk)\n",
    "        k += 1\n",
    "    return L, supportData\n",
    "\n",
    "def generateRules(L, supportData, minConf=0.7):  #supportData is a dict coming from scanD\n",
    "    bigRuleList = []\n",
    "    for i in range(1, len(L)):#only get the sets with two or more items\n",
    "        for freqSet in L[i]:\n",
    "            H1 = [frozenset([item]) for item in freqSet]\n",
    "            if (i > 1):\n",
    "                rulesFromConseq(freqSet, H1, supportData, bigRuleList, minConf)\n",
    "            else:\n",
    "                calcConf(freqSet, H1, supportData, bigRuleList, minConf)\n",
    "    return bigRuleList         \n",
    "\n",
    "def calcConf(freqSet, H, supportData, brl, minConf=0.7):\n",
    "    prunedH = [] #create new list to return\n",
    "    for conseq in H:\n",
    "        conf = supportData[freqSet]/supportData[freqSet-conseq] #calc confidence\n",
    "        if conf >= minConf: \n",
    "            print((freqSet-conseq,'-->',conseq,'conf:',conf))\n",
    "            brl.append((freqSet-conseq, conseq, conf))\n",
    "            prunedH.append(conseq)\n",
    "    return prunedH\n",
    "\n",
    "def rulesFromConseq(freqSet, H, supportData, brl, minConf=0.7):\n",
    "    m = len(H[0])\n",
    "    if (len(freqSet) > (m + 1)): #try further merging\n",
    "        Hmp1 = aprioriGen(H, m+1)#create Hm+1 new candidates\n",
    "        Hmp1 = calcConf(freqSet, Hmp1, supportData, brl, minConf)\n",
    "        if (len(Hmp1) > 1):    #need at least two sets to merge\n",
    "            rulesFromConseq(freqSet, Hmp1, supportData, brl, minConf)\n",
    "            \n",
    "def pntRules(ruleList, itemMeaning):\n",
    "    for ruleTup in ruleList:\n",
    "        for item in ruleTup[0]:\n",
    "            print((itemMeaning[item]))\n",
    "        print(\"           -------->\")\n",
    "        for item in ruleTup[1]:\n",
    "            print((itemMeaning[item]))\n",
    "        print((\"confidence: %f\" % ruleTup[2]))\n",
    "        print()       #print a blank line"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 测试结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "频繁项集L： [frozenset({5}), frozenset({2}), frozenset({3}), frozenset({1})]\n",
      "所有候选项集的支持度信息： {frozenset({1}): 0.5, frozenset({3}): 0.75, frozenset({4}): 0.25, frozenset({2}): 0.75, frozenset({5}): 0.75}\n"
     ]
    }
   ],
   "source": [
    "if __name__ == '__main__':\n",
    "    # 导入数据集\n",
    "    myDat = loadDataSet()\n",
    "    # 构建第一个候选项集列表C1\n",
    "    C1 = createC1( myDat )\n",
    "    \n",
    "    # 构建集合表示的数据集 D\n",
    "    D = list(map( set, myDat ))\n",
    "    # 选择出支持度不小于0.5 的项集作为频繁项集\n",
    "    L, suppData = scanD( D, C1, 0.5 )\n",
    "   \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 单个数据项结果展示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[1, 3, 4], [2, 3, 5], [1, 2, 3, 5], [2, 5]]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 导入数据集\n",
    "dataSet = loadDataSet()\n",
    "dataSet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({1}),\n",
       " frozenset({2}),\n",
       " frozenset({3}),\n",
       " frozenset({4}),\n",
       " frozenset({5})]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 构建候选项集合C1\n",
    "C1 = createC1(dataSet)\n",
    "C1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{1, 3, 4}, {2, 3, 5}, {1, 2, 3, 5}, {2, 5}]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 转用集合表示数据集\n",
    "D = list(map(set, dataSet))\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({5}), frozenset({2}), frozenset({3}), frozenset({1})]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 过滤掉不满足最小支持度的项集，此处使用0.5 为最小支持度\n",
    "L1, suppData = scanD(D, C1, 0.5)\n",
    "L1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{frozenset({1}): 0.5,\n",
       " frozenset({3}): 0.75,\n",
       " frozenset({4}): 0.25,\n",
       " frozenset({2}): 0.75,\n",
       " frozenset({5}): 0.75}"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suppData"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 多个数据项结果展示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "频繁项集L： [[frozenset({5}), frozenset({2}), frozenset({3}), frozenset({1})], [frozenset({2, 3}), frozenset({3, 5}), frozenset({2, 5}), frozenset({1, 3})], [frozenset({2, 3, 5})], []]\n"
     ]
    }
   ],
   "source": [
    "L, suppData = apriori(dataSet)\n",
    "# L为最小支持度默认为0.5 的频繁项集列表\n",
    "print(\"频繁项集L：\", L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "所有候选项集的支持度信息： {frozenset({1}): 0.5, frozenset({3}): 0.75, frozenset({4}): 0.25, frozenset({2}): 0.75, frozenset({5}): 0.75, frozenset({1, 3}): 0.5, frozenset({2, 5}): 0.75, frozenset({3, 5}): 0.5, frozenset({2, 3}): 0.5, frozenset({1, 5}): 0.25, frozenset({1, 2}): 0.25, frozenset({2, 3, 5}): 0.5}\n"
     ]
    }
   ],
   "source": [
    "print(\"所有候选项集的支持度信息：\", suppData)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 具体的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({5}), frozenset({2}), frozenset({3}), frozenset({1})]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({2, 3}), frozenset({3, 5}), frozenset({2, 5}), frozenset({1, 3})]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({2, 3, 5})]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[frozenset({2, 5}),\n",
       " frozenset({3, 5}),\n",
       " frozenset({1, 5}),\n",
       " frozenset({2, 3}),\n",
       " frozenset({1, 2}),\n",
       " frozenset({1, 3})]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# aprioriGen 函数工作流程\n",
    "aprioriGen(L[0], 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "#### 70%支持度结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[frozenset({5}), frozenset({2}), frozenset({3})], [frozenset({2, 5})], []]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L, suppData = apriori(dataSet, minSupport=0.7)\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 规则展示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### 0.7置信度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "hidden": true,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(frozenset({5}), '-->', frozenset({2}), 'conf:', 1.0)\n",
      "(frozenset({2}), '-->', frozenset({5}), 'conf:', 1.0)\n",
      "(frozenset({1}), '-->', frozenset({3}), 'conf:', 1.0)\n"
     ]
    }
   ],
   "source": [
    "dataSet = loadDataSet()\n",
    "# 先生成一个支持度为0.5的频繁项集合\n",
    "L, suppData = apriori(dataSet, minSupport=0.5)\n",
    "# 生成最小置信度为0.7的规则\n",
    "rules = generateRules(L, suppData, minConf=0.7)\n",
    "# rules\n",
    "#给出三条规则，观察知前两条可以互换前件和后件，但第三条不行"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "#### 降低为0.5置信度"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(frozenset({3}), '-->', frozenset({2}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({2}), '-->', frozenset({3}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({5}), '-->', frozenset({3}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({3}), '-->', frozenset({5}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({5}), '-->', frozenset({2}), 'conf:', 1.0)\n",
      "(frozenset({2}), '-->', frozenset({5}), 'conf:', 1.0)\n",
      "(frozenset({3}), '-->', frozenset({1}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({1}), '-->', frozenset({3}), 'conf:', 1.0)\n",
      "(frozenset({5}), '-->', frozenset({2, 3}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({3}), '-->', frozenset({2, 5}), 'conf:', 0.6666666666666666)\n",
      "(frozenset({2}), '-->', frozenset({3, 5}), 'conf:', 0.6666666666666666)\n"
     ]
    }
   ],
   "source": [
    "rules = generateRules(L, suppData, minConf=0.5)\n",
    "# 一旦降低可信度阈值，就可以获得更多的规则。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "### 毒蘑菇示例"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "C:\\Users\\wanzheng\\Desktop\\MLiA_SourceCode\\machinelearninginaction\\Ch11\n"
     ]
    }
   ],
   "source": [
    "cd C:\\Users\\wanzheng\\Desktop\\MLiA_SourceCode\\machinelearninginaction\\Ch11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'mushroom.dat 前几行如下：\\n\\n1 3 9 13 23 25 34 36 38 40 52 54 59 63 67 76 85 86 90 93 98 107 113 \\n2 3 9 14 23 26 34 36 39 40 52 55 59 63 67 76 85 86 90 93 99 108 114 \\n2 4 9 15 23 27 34 36 39 41 52 55 59 63 67 76 85 86 90 93 99 108 115 \\n1 3 10 15 23 25 34 36 38 41 52 54 59 63 67 76 85 86 90 93 98 107 113 \\n2 3 9 16 24 28 34 37 39 40 53 54 59 63 67 76 85 86 90 94 99 109 114 \\n\\n\\n第一个特征表示有毒或者可食用,如果有毒，则赋值为2。如果可食用则值为1\\n下一个特征是蘑菇伞的形状，共有6种可能，分别用3-8来表示。其他特征解释略过。\\n\\n'"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'''mushroom.dat 前几行如下：\n",
    "\n",
    "1 3 9 13 23 25 34 36 38 40 52 54 59 63 67 76 85 86 90 93 98 107 113 \n",
    "2 3 9 14 23 26 34 36 39 40 52 55 59 63 67 76 85 86 90 93 99 108 114 \n",
    "2 4 9 15 23 27 34 36 39 41 52 55 59 63 67 76 85 86 90 93 99 108 115 \n",
    "1 3 10 15 23 25 34 36 38 41 52 54 59 63 67 76 85 86 90 93 98 107 113 \n",
    "2 3 9 16 24 28 34 37 39 40 53 54 59 63 67 76 85 86 90 94 99 109 114 \n",
    "\n",
    "\n",
    "第一个特征表示有毒或者可食用,如果有毒，则赋值为2。如果可食用则值为1\n",
    "下一个特征是蘑菇伞的形状，共有6种可能，分别用3-8来表示。其他特征解释略过。\n",
    "\n",
    "'''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "# 加载数据集\n",
    "mushDatSet = [line.split() for line in open('mushroom.dat').readlines()]\n",
    "# 运行Apriori算法\n",
    "L, suppData = apriori(mushDatSet, minSupport=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[frozenset({'58'}),\n",
       "  frozenset({'56'}),\n",
       "  frozenset({'116'}),\n",
       "  frozenset({'6'}),\n",
       "  frozenset({'110'}),\n",
       "  frozenset({'94'}),\n",
       "  frozenset({'53'}),\n",
       "  frozenset({'28'}),\n",
       "  frozenset({'24'}),\n",
       "  frozenset({'10'}),\n",
       "  frozenset({'39'}),\n",
       "  frozenset({'2'}),\n",
       "  frozenset({'93'}),\n",
       "  frozenset({'90'}),\n",
       "  frozenset({'9'}),\n",
       "  frozenset({'86'}),\n",
       "  frozenset({'85'}),\n",
       "  frozenset({'76'}),\n",
       "  frozenset({'67'}),\n",
       "  frozenset({'63'}),\n",
       "  frozenset({'59'}),\n",
       "  frozenset({'52'}),\n",
       "  frozenset({'38'}),\n",
       "  frozenset({'36'}),\n",
       "  frozenset({'34'}),\n",
       "  frozenset({'3'}),\n",
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       "  frozenset({'2', '85', '86'}),\n",
       "  frozenset({'2', '76', '86'}),\n",
       "  frozenset({'2', '67', '86'}),\n",
       "  frozenset({'2', '63', '86'}),\n",
       "  frozenset({'2', '59', '86'}),\n",
       "  frozenset({'2', '36', '86'}),\n",
       "  frozenset({'2', '34', '86'}),\n",
       "  frozenset({'2', '23', '86'}),\n",
       "  frozenset({'2', '39', '86'}),\n",
       "  frozenset({'2', '85', '93'}),\n",
       "  frozenset({'2', '76', '85'}),\n",
       "  frozenset({'2', '67', '85'}),\n",
       "  frozenset({'2', '34', '67'}),\n",
       "  frozenset({'2', '39', '67'}),\n",
       "  frozenset({'2', '63', '93'}),\n",
       "  frozenset({'2', '63', '90'}),\n",
       "  frozenset({'2', '63', '85'}),\n",
       "  frozenset({'2', '59', '63'}),\n",
       "  frozenset({'2', '36', '63'}),\n",
       "  frozenset({'2', '34', '63'}),\n",
       "  frozenset({'2', '23', '63'}),\n",
       "  frozenset({'2', '39', '63'}),\n",
       "  frozenset({'2', '59', '93'}),\n",
       "  frozenset({'2', '59', '85'}),\n",
       "  frozenset({'2', '34', '59'}),\n",
       "  frozenset({'2', '23', '59'}),\n",
       "  frozenset({'2', '36', '93'}),\n",
       "  frozenset({'2', '36', '90'}),\n",
       "  frozenset({'2', '36', '85'}),\n",
       "  frozenset({'2', '36', '59'}),\n",
       "  frozenset({'2', '34', '36'}),\n",
       "  frozenset({'2', '23', '36'}),\n",
       "  frozenset({'2', '36', '39'}),\n",
       "  frozenset({'2', '34', '93'}),\n",
       "  frozenset({'2', '34', '85'}),\n",
       "  frozenset({'2', '34', '76'}),\n",
       "  frozenset({'2', '23', '93'}),\n",
       "  frozenset({'2', '23', '85'}),\n",
       "  frozenset({'2', '23', '34'}),\n",
       "  frozenset({'86', '90', '93'}),\n",
       "  frozenset({'85', '90', '93'}),\n",
       "  frozenset({'76', '85', '90'}),\n",
       "  frozenset({'63', '90', '93'}),\n",
       "  frozenset({'59', '90', '93'}),\n",
       "  frozenset({'59', '85', '90'}),\n",
       "  frozenset({'59', '76', '90'}),\n",
       "  frozenset({'38', '85', '90'}),\n",
       "  frozenset({'36', '90', '93'}),\n",
       "  frozenset({'34', '90', '93'}),\n",
       "  frozenset({'34', '85', '90'}),\n",
       "  frozenset({'34', '76', '90'}),\n",
       "  frozenset({'34', '59', '90'}),\n",
       "  frozenset({'34', '38', '90'}),\n",
       "  frozenset({'3', '85', '90'}),\n",
       "  frozenset({'3', '34', '90'}),\n",
       "  frozenset({'23', '90', '93'}),\n",
       "  frozenset({'23', '85', '90'}),\n",
       "  frozenset({'23', '59', '90'}),\n",
       "  frozenset({'23', '34', '90'}),\n",
       "  frozenset({'1', '85', '90'}),\n",
       "  frozenset({'1', '34', '90'}),\n",
       "  frozenset({'85', '86', '93'}),\n",
       "  frozenset({'85', '86', '90'}),\n",
       "  frozenset({'76', '86', '93'}),\n",
       "  frozenset({'76', '86', '90'}),\n",
       "  frozenset({'76', '85', '86'}),\n",
       "  frozenset({'67', '86', '93'}),\n",
       "  frozenset({'67', '86', '90'}),\n",
       "  frozenset({'67', '85', '86'}),\n",
       "  frozenset({'67', '76', '86'}),\n",
       "  frozenset({'63', '86', '93'}),\n",
       "  frozenset({'63', '86', '90'}),\n",
       "  frozenset({'63', '85', '86'}),\n",
       "  frozenset({'63', '76', '86'}),\n",
       "  frozenset({'63', '67', '86'}),\n",
       "  frozenset({'59', '86', '93'}),\n",
       "  frozenset({'59', '86', '90'}),\n",
       "  frozenset({'59', '85', '86'}),\n",
       "  frozenset({'59', '76', '86'}),\n",
       "  frozenset({'59', '67', '86'}),\n",
       "  frozenset({'59', '63', '86'}),\n",
       "  frozenset({'52', '86', '90'}),\n",
       "  frozenset({'52', '85', '86'}),\n",
       "  frozenset({'38', '86', '90'}),\n",
       "  frozenset({'38', '85', '86'}),\n",
       "  frozenset({'36', '86', '93'}),\n",
       "  frozenset({'36', '86', '90'}),\n",
       "  frozenset({'36', '85', '86'}),\n",
       "  frozenset({'36', '76', '86'}),\n",
       "  frozenset({'36', '67', '86'}),\n",
       "  frozenset({'36', '63', '86'}),\n",
       "  frozenset({'36', '59', '86'}),\n",
       "  frozenset({'36', '52', '86'}),\n",
       "  frozenset({'34', '86', '93'}),\n",
       "  frozenset({'34', '86', '90'}),\n",
       "  frozenset({'34', '85', '86'}),\n",
       "  frozenset({'34', '76', '86'}),\n",
       "  frozenset({'34', '67', '86'}),\n",
       "  frozenset({'34', '63', '86'}),\n",
       "  frozenset({'34', '59', '86'}),\n",
       "  frozenset({'34', '52', '86'}),\n",
       "  frozenset({'34', '38', '86'}),\n",
       "  frozenset({'34', '36', '86'}),\n",
       "  frozenset({'3', '86', '90'}),\n",
       "  frozenset({'3', '85', '86'}),\n",
       "  frozenset({'3', '36', '86'}),\n",
       "  frozenset({'3', '34', '86'}),\n",
       "  frozenset({'23', '86', '93'}),\n",
       "  frozenset({'23', '86', '90'}),\n",
       "  frozenset({'23', '85', '86'}),\n",
       "  frozenset({'23', '63', '86'}),\n",
       "  frozenset({'23', '59', '86'}),\n",
       "  frozenset({'23', '36', '86'}),\n",
       "  frozenset({'23', '34', '86'}),\n",
       "  frozenset({'1', '86', '90'}),\n",
       "  frozenset({'1', '85', '86'}),\n",
       "  frozenset({'1', '36', '86'}),\n",
       "  frozenset({'1', '34', '86'}),\n",
       "  frozenset({'76', '85', '93'}),\n",
       "  frozenset({'67', '85', '93'}),\n",
       "  frozenset({'67', '85', '90'}),\n",
       "  frozenset({'63', '85', '93'}),\n",
       "  frozenset({'63', '85', '90'}),\n",
       "  frozenset({'59', '85', '93'}),\n",
       "  frozenset({'52', '85', '90'}),\n",
       "  frozenset({'36', '85', '93'}),\n",
       "  frozenset({'36', '85', '90'}),\n",
       "  frozenset({'34', '85', '93'}),\n",
       "  frozenset({'23', '85', '93'}),\n",
       "  frozenset({'67', '76', '90'}),\n",
       "  frozenset({'67', '76', '85'}),\n",
       "  frozenset({'63', '76', '90'}),\n",
       "  frozenset({'63', '76', '85'}),\n",
       "  frozenset({'59', '76', '85'}),\n",
       "  frozenset({'36', '76', '90'}),\n",
       "  frozenset({'36', '76', '85'}),\n",
       "  frozenset({'34', '76', '93'}),\n",
       "  frozenset({'34', '76', '85'}),\n",
       "  frozenset({'63', '67', '90'}),\n",
       "  frozenset({'63', '67', '85'}),\n",
       "  frozenset({'59', '67', '90'}),\n",
       "  frozenset({'59', '67', '85'}),\n",
       "  frozenset({'59', '67', '76'}),\n",
       "  frozenset({'59', '63', '67'}),\n",
       "  frozenset({'36', '67', '90'}),\n",
       "  frozenset({'36', '67', '85'}),\n",
       "  frozenset({'36', '59', '67'}),\n",
       "  frozenset({'34', '67', '93'}),\n",
       "  frozenset({'34', '67', '90'}),\n",
       "  frozenset({'34', '67', '85'}),\n",
       "  frozenset({'34', '67', '76'}),\n",
       "  frozenset({'34', '63', '67'}),\n",
       "  frozenset({'34', '59', '67'}),\n",
       "  frozenset({'34', '36', '67'}),\n",
       "  frozenset({'59', '63', '93'}),\n",
       "  frozenset({'59', '63', '90'}),\n",
       "  frozenset({'59', '63', '85'}),\n",
       "  frozenset({'59', '63', '76'}),\n",
       "  frozenset({'36', '63', '93'}),\n",
       "  frozenset({'36', '63', '90'}),\n",
       "  frozenset({'36', '63', '85'}),\n",
       "  frozenset({'36', '59', '63'}),\n",
       "  frozenset({'34', '63', '93'}),\n",
       "  frozenset({'34', '63', '90'}),\n",
       "  frozenset({'34', '63', '85'}),\n",
       "  frozenset({'34', '63', '76'}),\n",
       "  frozenset({'34', '59', '63'}),\n",
       "  frozenset({'34', '36', '63'}),\n",
       "  frozenset({'23', '63', '93'}),\n",
       "  frozenset({'23', '63', '90'}),\n",
       "  frozenset({'23', '63', '85'}),\n",
       "  frozenset({'23', '59', '63'}),\n",
       "  frozenset({'23', '36', '63'}),\n",
       "  frozenset({'23', '34', '63'}),\n",
       "  frozenset({'36', '59', '93'}),\n",
       "  frozenset({'36', '59', '90'}),\n",
       "  frozenset({'36', '59', '85'}),\n",
       "  frozenset({'36', '59', '76'}),\n",
       "  frozenset({'34', '59', '93'}),\n",
       "  frozenset({'34', '59', '85'}),\n",
       "  frozenset({'34', '59', '76'}),\n",
       "  frozenset({'23', '59', '93'}),\n",
       "  frozenset({'23', '59', '85'}),\n",
       "  frozenset({'23', '34', '59'}),\n",
       "  frozenset({'36', '52', '90'}),\n",
       "  frozenset({'36', '52', '85'}),\n",
       "  frozenset({'34', '52', '90'}),\n",
       "  frozenset({'34', '52', '85'}),\n",
       "  frozenset({'34', '36', '52'}),\n",
       "  frozenset({'34', '38', '85'}),\n",
       "  frozenset({'34', '36', '93'}),\n",
       "  frozenset({'34', '36', '90'}),\n",
       "  frozenset({'34', '36', '85'}),\n",
       "  frozenset({'34', '36', '76'}),\n",
       "  frozenset({'34', '36', '59'}),\n",
       "  frozenset({'3', '36', '90'}),\n",
       "  frozenset({'3', '36', '85'}),\n",
       "  frozenset({'3', '34', '36'}),\n",
       "  frozenset({'23', '36', '93'}),\n",
       "  frozenset({'23', '36', '90'}),\n",
       "  frozenset({'23', '36', '85'}),\n",
       "  frozenset({'23', '36', '59'}),\n",
       "  frozenset({'23', '34', '36'}),\n",
       "  frozenset({'1', '36', '90'}),\n",
       "  frozenset({'1', '36', '85'}),\n",
       "  frozenset({'1', '34', '36'}),\n",
       "  frozenset({'3', '34', '85'}),\n",
       "  frozenset({'23', '34', '93'}),\n",
       "  frozenset({'23', '34', '85'}),\n",
       "  frozenset({'1', '34', '85'})],\n",
       " [frozenset({'1', '110', '24', '36'}),\n",
       "  frozenset({'1', '110', '24', '34'}),\n",
       "  frozenset({'1', '110', '24', '85'}),\n",
       "  frozenset({'1', '110', '24', '90'}),\n",
       "  frozenset({'1', '110', '24', '86'}),\n",
       "  frozenset({'1', '24', '34', '85'}),\n",
       "  frozenset({'1', '24', '34', '86'}),\n",
       "  frozenset({'1', '24', '85', '86'}),\n",
       "  frozenset({'1', '24', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '90'}),\n",
       "  frozenset({'1', '24', '85', '90'}),\n",
       "  frozenset({'1', '24', '34', '36'}),\n",
       "  frozenset({'1', '24', '36', '85'}),\n",
       "  frozenset({'1', '24', '36', '90'}),\n",
       "  frozenset({'1', '24', '36', '86'}),\n",
       "  frozenset({'110', '36', '53', '86'}),\n",
       "  frozenset({'110', '34', '36', '53'}),\n",
       "  frozenset({'110', '36', '53', '85'}),\n",
       "  frozenset({'110', '36', '53', '90'}),\n",
       "  frozenset({'36', '53', '63', '86'}),\n",
       "  frozenset({'36', '53', '86', '90'}),\n",
       "  frozenset({'36', '56', '86', '90'}),\n",
       "  frozenset({'39', '56', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '59'}),\n",
       "  frozenset({'34', '36', '53', '85'}),\n",
       "  frozenset({'36', '53', '59', '85'}),\n",
       "  frozenset({'34', '36', '53', '90'}),\n",
       "  frozenset({'36', '53', '59', '90'}),\n",
       "  frozenset({'36', '53', '85', '90'}),\n",
       "  frozenset({'116', '34', '36', '85'}),\n",
       "  frozenset({'116', '34', '36', '90'}),\n",
       "  frozenset({'116', '36', '85', '90'}),\n",
       "  frozenset({'34', '36', '56', '85'}),\n",
       "  frozenset({'34', '36', '56', '90'}),\n",
       "  frozenset({'36', '56', '85', '90'}),\n",
       "  frozenset({'34', '39', '56', '85'}),\n",
       "  frozenset({'116', '34', '36', '86'}),\n",
       "  frozenset({'116', '36', '85', '86'}),\n",
       "  frozenset({'116', '36', '86', '90'}),\n",
       "  frozenset({'34', '39', '56', '86'}),\n",
       "  frozenset({'39', '56', '85', '86'}),\n",
       "  frozenset({'34', '36', '56', '86'}),\n",
       "  frozenset({'36', '56', '85', '86'}),\n",
       "  frozenset({'36', '39', '56', '86'}),\n",
       "  frozenset({'34', '36', '53', '63'}),\n",
       "  frozenset({'36', '53', '63', '85'}),\n",
       "  frozenset({'36', '53', '63', '90'}),\n",
       "  frozenset({'34', '36', '53', '86'}),\n",
       "  frozenset({'36', '53', '59', '86'}),\n",
       "  frozenset({'36', '53', '85', '86'}),\n",
       "  frozenset({'110', '24', '34', '85'}),\n",
       "  frozenset({'110', '24', '34', '36'}),\n",
       "  frozenset({'110', '24', '36', '85'}),\n",
       "  frozenset({'110', '24', '36', '90'}),\n",
       "  frozenset({'110', '24', '34', '90'}),\n",
       "  frozenset({'110', '24', '85', '90'}),\n",
       "  frozenset({'110', '24', '34', '86'}),\n",
       "  frozenset({'110', '24', '36', '86'}),\n",
       "  frozenset({'110', '24', '85', '86'}),\n",
       "  frozenset({'110', '24', '86', '90'}),\n",
       "  frozenset({'110', '34', '53', '85'}),\n",
       "  frozenset({'110', '34', '53', '90'}),\n",
       "  frozenset({'110', '53', '85', '90'}),\n",
       "  frozenset({'116', '34', '56', '85'}),\n",
       "  frozenset({'116', '34', '85', '90'}),\n",
       "  frozenset({'116', '34', '56', '86'}),\n",
       "  frozenset({'116', '56', '85', '86'}),\n",
       "  frozenset({'116', '34', '85', '86'}),\n",
       "  frozenset({'116', '56', '86', '90'}),\n",
       "  frozenset({'116', '34', '86', '90'}),\n",
       "  frozenset({'116', '85', '86', '90'}),\n",
       "  frozenset({'116', '34', '56', '90'}),\n",
       "  frozenset({'116', '56', '85', '90'}),\n",
       "  frozenset({'34', '56', '85', '86'}),\n",
       "  frozenset({'34', '56', '86', '90'}),\n",
       "  frozenset({'56', '85', '86', '90'}),\n",
       "  frozenset({'34', '56', '85', '90'}),\n",
       "  frozenset({'110', '34', '53', '86'}),\n",
       "  frozenset({'110', '53', '85', '86'}),\n",
       "  frozenset({'110', '53', '86', '90'}),\n",
       "  frozenset({'34', '36', '6', '85'}),\n",
       "  frozenset({'34', '36', '6', '86'}),\n",
       "  frozenset({'36', '6', '85', '86'}),\n",
       "  frozenset({'34', '36', '6', '90'}),\n",
       "  frozenset({'36', '6', '85', '90'}),\n",
       "  frozenset({'36', '6', '86', '90'}),\n",
       "  frozenset({'34', '6', '85', '86'}),\n",
       "  frozenset({'34', '6', '85', '90'}),\n",
       "  frozenset({'34', '6', '86', '90'}),\n",
       "  frozenset({'6', '85', '86', '90'}),\n",
       "  frozenset({'24', '36', '86', '90'}),\n",
       "  frozenset({'24', '34', '36', '85'}),\n",
       "  frozenset({'24', '34', '36', '90'}),\n",
       "  frozenset({'24', '36', '85', '90'}),\n",
       "  frozenset({'24', '34', '36', '86'}),\n",
       "  frozenset({'24', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '34', '36'}),\n",
       "  frozenset({'1', '110', '34', '85'}),\n",
       "  frozenset({'1', '110', '34', '90'}),\n",
       "  frozenset({'1', '110', '36', '85'}),\n",
       "  frozenset({'110', '34', '36', '85'}),\n",
       "  frozenset({'1', '110', '36', '90'}),\n",
       "  frozenset({'110', '34', '36', '90'}),\n",
       "  frozenset({'110', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '85', '90'}),\n",
       "  frozenset({'110', '34', '85', '90'}),\n",
       "  frozenset({'1', '110', '34', '86'}),\n",
       "  frozenset({'1', '110', '36', '86'}),\n",
       "  frozenset({'110', '34', '36', '86'}),\n",
       "  frozenset({'1', '110', '85', '86'}),\n",
       "  frozenset({'110', '34', '85', '86'}),\n",
       "  frozenset({'110', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '86', '90'}),\n",
       "  frozenset({'110', '34', '86', '90'}),\n",
       "  frozenset({'110', '36', '86', '90'}),\n",
       "  frozenset({'110', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '85', '86'}),\n",
       "  frozenset({'24', '34', '86', '90'}),\n",
       "  frozenset({'24', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '85'}),\n",
       "  frozenset({'28', '34', '59', '85'}),\n",
       "  frozenset({'28', '59', '63', '85'}),\n",
       "  frozenset({'28', '59', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '59'}),\n",
       "  frozenset({'2', '28', '59', '63'}),\n",
       "  frozenset({'2', '28', '59', '85'}),\n",
       "  frozenset({'2', '28', '59', '90'}),\n",
       "  frozenset({'28', '34', '39', '59'}),\n",
       "  frozenset({'28', '39', '59', '63'}),\n",
       "  frozenset({'28', '39', '59', '85'}),\n",
       "  frozenset({'2', '28', '39', '59'}),\n",
       "  frozenset({'28', '34', '63', '85'}),\n",
       "  frozenset({'2', '28', '34', '63'}),\n",
       "  frozenset({'2', '28', '63', '85'}),\n",
       "  frozenset({'28', '34', '39', '63'}),\n",
       "  frozenset({'28', '34', '85', '90'}),\n",
       "  frozenset({'28', '34', '39', '85'}),\n",
       "  frozenset({'28', '39', '63', '85'}),\n",
       "  frozenset({'28', '34', '53', '85'}),\n",
       "  frozenset({'2', '28', '53', '86'}),\n",
       "  frozenset({'28', '39', '53', '86'}),\n",
       "  frozenset({'2', '28', '39', '86'}),\n",
       "  frozenset({'28', '34', '53', '86'}),\n",
       "  frozenset({'2', '28', '34', '86'}),\n",
       "  frozenset({'28', '34', '39', '86'}),\n",
       "  frozenset({'2', '28', '59', '86'}),\n",
       "  frozenset({'28', '39', '59', '86'}),\n",
       "  frozenset({'28', '34', '59', '86'}),\n",
       "  frozenset({'2', '28', '63', '86'}),\n",
       "  frozenset({'28', '39', '63', '86'}),\n",
       "  frozenset({'28', '34', '63', '86'}),\n",
       "  frozenset({'28', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '85', '86'}),\n",
       "  frozenset({'28', '39', '85', '86'}),\n",
       "  frozenset({'28', '34', '85', '86'}),\n",
       "  frozenset({'28', '59', '85', '86'}),\n",
       "  frozenset({'28', '63', '85', '86'}),\n",
       "  frozenset({'28', '53', '86', '90'}),\n",
       "  frozenset({'2', '28', '86', '90'}),\n",
       "  frozenset({'28', '39', '86', '90'}),\n",
       "  frozenset({'28', '34', '86', '90'}),\n",
       "  frozenset({'28', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '90'}),\n",
       "  frozenset({'2', '28', '85', '90'}),\n",
       "  frozenset({'28', '34', '39', '90'}),\n",
       "  frozenset({'28', '39', '85', '90'}),\n",
       "  frozenset({'2', '28', '39', '90'}),\n",
       "  frozenset({'28', '34', '53', '90'}),\n",
       "  frozenset({'28', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '53', '90'}),\n",
       "  frozenset({'28', '39', '53', '90'}),\n",
       "  frozenset({'2', '28', '34', '39'}),\n",
       "  frozenset({'2', '28', '39', '63'}),\n",
       "  frozenset({'2', '28', '39', '85'}),\n",
       "  frozenset({'2', '28', '34', '53'}),\n",
       "  frozenset({'2', '28', '53', '85'}),\n",
       "  frozenset({'28', '34', '39', '53'}),\n",
       "  frozenset({'28', '39', '53', '85'}),\n",
       "  frozenset({'2', '28', '39', '53'}),\n",
       "  frozenset({'34', '53', '59', '85'}),\n",
       "  frozenset({'34', '53', '76', '85'}),\n",
       "  frozenset({'2', '34', '53', '85'}),\n",
       "  frozenset({'34', '39', '53', '85'}),\n",
       "  frozenset({'2', '34', '39', '53'}),\n",
       "  frozenset({'24', '34', '53', '85'}),\n",
       "  frozenset({'34', '53', '59', '63'}),\n",
       "  frozenset({'34', '53', '63', '85'}),\n",
       "  frozenset({'53', '59', '63', '85'}),\n",
       "  frozenset({'34', '53', '63', '90'}),\n",
       "  frozenset({'53', '59', '63', '90'}),\n",
       "  frozenset({'53', '63', '85', '90'}),\n",
       "  frozenset({'34', '53', '67', '85'}),\n",
       "  frozenset({'34', '53', '67', '90'}),\n",
       "  frozenset({'53', '67', '85', '90'}),\n",
       "  frozenset({'2', '39', '53', '86'}),\n",
       "  frozenset({'24', '34', '53', '86'}),\n",
       "  frozenset({'2', '34', '53', '86'}),\n",
       "  frozenset({'34', '39', '53', '86'}),\n",
       "  frozenset({'34', '53', '59', '86'}),\n",
       "  frozenset({'34', '53', '63', '86'}),\n",
       "  frozenset({'53', '59', '63', '86'}),\n",
       "  frozenset({'53', '63', '85', '86'}),\n",
       "  frozenset({'53', '63', '86', '90'}),\n",
       "  frozenset({'34', '53', '67', '86'}),\n",
       "  frozenset({'34', '53', '76', '86'}),\n",
       "  frozenset({'24', '53', '85', '86'}),\n",
       "  frozenset({'2', '53', '85', '86'}),\n",
       "  frozenset({'39', '53', '85', '86'}),\n",
       "  frozenset({'34', '53', '85', '86'}),\n",
       "  frozenset({'53', '59', '85', '86'}),\n",
       "  frozenset({'53', '67', '85', '86'}),\n",
       "  frozenset({'53', '76', '85', '86'}),\n",
       "  frozenset({'34', '53', '86', '90'}),\n",
       "  frozenset({'53', '59', '86', '90'}),\n",
       "  frozenset({'53', '67', '86', '90'}),\n",
       "  frozenset({'53', '76', '86', '90'}),\n",
       "  frozenset({'53', '85', '86', '90'}),\n",
       "  frozenset({'2', '53', '86', '90'}),\n",
       "  frozenset({'39', '53', '86', '90'}),\n",
       "  frozenset({'24', '53', '86', '90'}),\n",
       "  frozenset({'2', '39', '53', '90'}),\n",
       "  frozenset({'2', '34', '53', '90'}),\n",
       "  frozenset({'34', '39', '53', '90'}),\n",
       "  frozenset({'34', '53', '59', '90'}),\n",
       "  frozenset({'34', '53', '76', '90'}),\n",
       "  frozenset({'2', '53', '85', '90'}),\n",
       "  frozenset({'39', '53', '85', '90'}),\n",
       "  frozenset({'34', '53', '85', '90'}),\n",
       "  frozenset({'53', '59', '85', '90'}),\n",
       "  frozenset({'53', '76', '85', '90'}),\n",
       "  frozenset({'2', '39', '53', '85'}),\n",
       "  frozenset({'34', '85', '86', '94'}),\n",
       "  frozenset({'24', '34', '85', '94'}),\n",
       "  frozenset({'24', '34', '86', '94'}),\n",
       "  frozenset({'34', '85', '90', '94'}),\n",
       "  frozenset({'24', '85', '86', '94'}),\n",
       "  frozenset({'34', '53', '85', '94'}),\n",
       "  frozenset({'34', '86', '90', '94'}),\n",
       "  frozenset({'85', '86', '90', '94'}),\n",
       "  frozenset({'34', '53', '86', '94'}),\n",
       "  frozenset({'53', '85', '86', '94'}),\n",
       "  frozenset({'24', '34', '90', '94'}),\n",
       "  frozenset({'24', '85', '90', '94'}),\n",
       "  frozenset({'24', '86', '90', '94'}),\n",
       "  frozenset({'34', '53', '90', '94'}),\n",
       "  frozenset({'53', '85', '90', '94'}),\n",
       "  frozenset({'53', '86', '90', '94'}),\n",
       "  frozenset({'24', '53', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '94'}),\n",
       "  frozenset({'24', '53', '85', '94'}),\n",
       "  frozenset({'24', '53', '86', '94'}),\n",
       "  frozenset({'10', '34', '36', '85'}),\n",
       "  frozenset({'10', '34', '36', '90'}),\n",
       "  frozenset({'10', '36', '85', '90'}),\n",
       "  frozenset({'10', '34', '85', '86'}),\n",
       "  frozenset({'10', '34', '36', '86'}),\n",
       "  frozenset({'10', '36', '85', '86'}),\n",
       "  frozenset({'10', '34', '86', '90'}),\n",
       "  frozenset({'10', '36', '86', '90'}),\n",
       "  frozenset({'10', '85', '86', '90'}),\n",
       "  frozenset({'10', '34', '85', '90'}),\n",
       "  frozenset({'2', '23', '34', '85'}),\n",
       "  frozenset({'2', '23', '34', '93'}),\n",
       "  frozenset({'2', '23', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '36'}),\n",
       "  frozenset({'2', '23', '36', '59'}),\n",
       "  frozenset({'2', '23', '36', '85'}),\n",
       "  frozenset({'2', '23', '36', '93'}),\n",
       "  frozenset({'2', '34', '36', '39'}),\n",
       "  frozenset({'2', '36', '39', '59'}),\n",
       "  frozenset({'2', '34', '36', '59'}),\n",
       "  frozenset({'2', '36', '39', '85'}),\n",
       "  frozenset({'2', '34', '36', '85'}),\n",
       "  frozenset({'2', '36', '59', '85'}),\n",
       "  frozenset({'2', '34', '36', '90'}),\n",
       "  frozenset({'2', '36', '85', '90'}),\n",
       "  frozenset({'2', '36', '90', '93'}),\n",
       "  frozenset({'2', '36', '39', '93'}),\n",
       "  frozenset({'2', '34', '36', '93'}),\n",
       "  frozenset({'2', '36', '59', '93'}),\n",
       "  frozenset({'2', '36', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '59'}),\n",
       "  frozenset({'2', '23', '59', '85'}),\n",
       "  frozenset({'2', '23', '59', '93'}),\n",
       "  frozenset({'2', '34', '59', '85'}),\n",
       "  frozenset({'2', '34', '59', '93'}),\n",
       "  frozenset({'2', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '63'}),\n",
       "  frozenset({'2', '23', '63', '85'}),\n",
       "  frozenset({'2', '23', '36', '63'}),\n",
       "  frozenset({'2', '34', '36', '63'}),\n",
       "  frozenset({'2', '36', '59', '63'}),\n",
       "  frozenset({'2', '36', '63', '85'}),\n",
       "  frozenset({'2', '36', '63', '90'}),\n",
       "  frozenset({'2', '36', '63', '93'}),\n",
       "  frozenset({'2', '23', '59', '63'}),\n",
       "  frozenset({'2', '34', '59', '63'}),\n",
       "  frozenset({'2', '59', '63', '85'}),\n",
       "  frozenset({'2', '59', '63', '90'}),\n",
       "  frozenset({'2', '59', '63', '93'}),\n",
       "  frozenset({'2', '34', '63', '85'}),\n",
       "  frozenset({'2', '34', '63', '90'}),\n",
       "  frozenset({'2', '63', '85', '90'}),\n",
       "  frozenset({'2', '63', '90', '93'}),\n",
       "  frozenset({'2', '34', '63', '93'}),\n",
       "  frozenset({'2', '63', '85', '93'}),\n",
       "  frozenset({'2', '34', '67', '85'}),\n",
       "  frozenset({'2', '34', '76', '85'}),\n",
       "  frozenset({'2', '34', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '86'}),\n",
       "  frozenset({'2', '23', '85', '86'}),\n",
       "  frozenset({'2', '23', '86', '93'}),\n",
       "  frozenset({'2', '23', '36', '86'}),\n",
       "  frozenset({'2', '34', '36', '86'}),\n",
       "  frozenset({'2', '36', '59', '86'}),\n",
       "  frozenset({'2', '36', '85', '86'}),\n",
       "  frozenset({'2', '36', '86', '93'}),\n",
       "  frozenset({'2', '23', '59', '86'}),\n",
       "  frozenset({'2', '34', '59', '86'}),\n",
       "  frozenset({'2', '59', '85', '86'}),\n",
       "  frozenset({'2', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '63', '86'}),\n",
       "  frozenset({'2', '34', '63', '86'}),\n",
       "  frozenset({'2', '36', '63', '86'}),\n",
       "  frozenset({'2', '59', '63', '86'}),\n",
       "  frozenset({'2', '63', '85', '86'}),\n",
       "  frozenset({'2', '63', '86', '90'}),\n",
       "  frozenset({'2', '63', '86', '93'}),\n",
       "  frozenset({'2', '34', '67', '86'}),\n",
       "  frozenset({'2', '34', '76', '86'}),\n",
       "  frozenset({'2', '34', '85', '86'}),\n",
       "  frozenset({'2', '67', '85', '86'}),\n",
       "  frozenset({'2', '76', '85', '86'}),\n",
       "  frozenset({'2', '23', '86', '90'}),\n",
       "  frozenset({'2', '34', '86', '90'}),\n",
       "  frozenset({'2', '36', '86', '90'}),\n",
       "  frozenset({'2', '59', '86', '90'}),\n",
       "  frozenset({'2', '85', '86', '90'}),\n",
       "  frozenset({'2', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '86', '93'}),\n",
       "  frozenset({'2', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '90'}),\n",
       "  frozenset({'2', '23', '59', '90'}),\n",
       "  frozenset({'2', '23', '85', '90'}),\n",
       "  frozenset({'2', '23', '90', '93'}),\n",
       "  frozenset({'2', '34', '39', '90'}),\n",
       "  frozenset({'2', '39', '59', '90'}),\n",
       "  frozenset({'2', '34', '59', '90'}),\n",
       "  frozenset({'2', '39', '85', '90'}),\n",
       "  frozenset({'2', '34', '85', '90'}),\n",
       "  frozenset({'2', '59', '85', '90'}),\n",
       "  frozenset({'2', '39', '90', '93'}),\n",
       "  frozenset({'2', '34', '90', '93'}),\n",
       "  frozenset({'2', '59', '90', '93'}),\n",
       "  frozenset({'2', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '59'}),\n",
       "  frozenset({'23', '34', '39', '85'}),\n",
       "  frozenset({'23', '39', '59', '85'}),\n",
       "  frozenset({'23', '34', '39', '93'}),\n",
       "  frozenset({'23', '39', '59', '93'}),\n",
       "  frozenset({'23', '39', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '39'}),\n",
       "  frozenset({'2', '23', '39', '59'}),\n",
       "  frozenset({'2', '23', '39', '85'}),\n",
       "  frozenset({'2', '23', '39', '93'}),\n",
       "  frozenset({'3', '34', '39', '85'}),\n",
       "  frozenset({'34', '39', '59', '85'}),\n",
       "  frozenset({'34', '39', '76', '85'}),\n",
       "  frozenset({'34', '39', '59', '93'}),\n",
       "  frozenset({'34', '39', '85', '93'}),\n",
       "  frozenset({'2', '34', '39', '59'}),\n",
       "  frozenset({'2', '34', '39', '76'}),\n",
       "  frozenset({'2', '34', '39', '85'}),\n",
       "  frozenset({'2', '34', '39', '93'}),\n",
       "  frozenset({'23', '34', '36', '39'}),\n",
       "  frozenset({'23', '36', '39', '59'}),\n",
       "  frozenset({'34', '36', '39', '59'}),\n",
       "  frozenset({'23', '36', '39', '85'}),\n",
       "  frozenset({'34', '36', '39', '85'}),\n",
       "  frozenset({'36', '39', '59', '85'}),\n",
       "  frozenset({'23', '36', '39', '90'}),\n",
       "  frozenset({'34', '36', '39', '90'}),\n",
       "  frozenset({'36', '39', '59', '90'}),\n",
       "  frozenset({'36', '39', '85', '90'}),\n",
       "  frozenset({'23', '36', '39', '93'}),\n",
       "  frozenset({'34', '36', '39', '93'}),\n",
       "  frozenset({'36', '39', '59', '93'}),\n",
       "  frozenset({'36', '39', '85', '93'}),\n",
       "  frozenset({'36', '39', '90', '93'}),\n",
       "  frozenset({'36', '39', '52', '85'}),\n",
       "  frozenset({'34', '39', '52', '85'}),\n",
       "  frozenset({'2', '23', '39', '63'}),\n",
       "  frozenset({'2', '34', '39', '63'}),\n",
       "  frozenset({'23', '34', '39', '63'}),\n",
       "  frozenset({'2', '36', '39', '63'}),\n",
       "  frozenset({'23', '36', '39', '63'}),\n",
       "  frozenset({'34', '36', '39', '63'}),\n",
       "  frozenset({'2', '39', '59', '63'}),\n",
       "  frozenset({'23', '39', '59', '63'}),\n",
       "  frozenset({'34', '39', '59', '63'}),\n",
       "  frozenset({'36', '39', '59', '63'}),\n",
       "  frozenset({'2', '39', '63', '85'}),\n",
       "  frozenset({'23', '39', '63', '85'}),\n",
       "  frozenset({'34', '39', '63', '85'}),\n",
       "  frozenset({'36', '39', '63', '85'}),\n",
       "  frozenset({'39', '59', '63', '85'}),\n",
       "  frozenset({'2', '39', '63', '90'}),\n",
       "  frozenset({'34', '39', '63', '90'}),\n",
       "  frozenset({'36', '39', '63', '90'}),\n",
       "  frozenset({'39', '59', '63', '90'}),\n",
       "  frozenset({'39', '63', '85', '90'}),\n",
       "  frozenset({'2', '39', '63', '93'}),\n",
       "  frozenset({'23', '39', '63', '93'}),\n",
       "  frozenset({'34', '39', '63', '93'}),\n",
       "  frozenset({'36', '39', '63', '93'}),\n",
       "  frozenset({'39', '59', '63', '93'}),\n",
       "  frozenset({'39', '63', '85', '93'}),\n",
       "  frozenset({'39', '63', '90', '93'}),\n",
       "  frozenset({'2', '34', '39', '67'}),\n",
       "  frozenset({'2', '39', '67', '85'}),\n",
       "  frozenset({'34', '39', '67', '85'}),\n",
       "  frozenset({'39', '59', '85', '93'}),\n",
       "  frozenset({'2', '39', '59', '85'}),\n",
       "  frozenset({'2', '39', '76', '85'}),\n",
       "  frozenset({'2', '23', '39', '86'}),\n",
       "  frozenset({'2', '34', '39', '86'}),\n",
       "  frozenset({'23', '34', '39', '86'}),\n",
       "  frozenset({'3', '34', '39', '86'}),\n",
       "  frozenset({'23', '36', '39', '86'}),\n",
       "  frozenset({'34', '36', '39', '86'}),\n",
       "  frozenset({'36', '39', '59', '86'}),\n",
       "  frozenset({'36', '39', '85', '86'}),\n",
       "  frozenset({'36', '39', '86', '93'}),\n",
       "  frozenset({'2', '36', '39', '86'}),\n",
       "  frozenset({'34', '39', '52', '86'}),\n",
       "  frozenset({'2', '39', '59', '86'}),\n",
       "  frozenset({'23', '39', '59', '86'}),\n",
       "  frozenset({'34', '39', '59', '86'}),\n",
       "  frozenset({'23', '39', '63', '86'}),\n",
       "  frozenset({'34', '39', '63', '86'}),\n",
       "  frozenset({'36', '39', '63', '86'}),\n",
       "  frozenset({'39', '59', '63', '86'}),\n",
       "  frozenset({'39', '63', '85', '86'}),\n",
       "  frozenset({'39', '63', '86', '90'}),\n",
       "  frozenset({'39', '63', '86', '93'}),\n",
       "  frozenset({'2', '39', '63', '86'}),\n",
       "  frozenset({'2', '39', '67', '86'}),\n",
       "  frozenset({'34', '39', '67', '86'}),\n",
       "  frozenset({'2', '39', '76', '86'}),\n",
       "  frozenset({'34', '39', '76', '86'}),\n",
       "  frozenset({'2', '39', '85', '86'}),\n",
       "  frozenset({'23', '39', '85', '86'}),\n",
       "  frozenset({'3', '39', '85', '86'}),\n",
       "  frozenset({'34', '39', '85', '86'}),\n",
       "  frozenset({'39', '52', '85', '86'}),\n",
       "  frozenset({'39', '59', '85', '86'}),\n",
       "  frozenset({'39', '67', '85', '86'}),\n",
       "  frozenset({'39', '76', '85', '86'}),\n",
       "  frozenset({'23', '39', '86', '90'}),\n",
       "  frozenset({'34', '39', '86', '90'}),\n",
       "  frozenset({'36', '39', '86', '90'}),\n",
       "  frozenset({'39', '59', '86', '90'}),\n",
       "  frozenset({'39', '85', '86', '90'}),\n",
       "  frozenset({'39', '86', '90', '93'}),\n",
       "  frozenset({'2', '39', '86', '90'}),\n",
       "  frozenset({'2', '39', '86', '93'}),\n",
       "  frozenset({'23', '39', '86', '93'}),\n",
       "  frozenset({'34', '39', '86', '93'}),\n",
       "  frozenset({'39', '59', '86', '93'}),\n",
       "  frozenset({'39', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '90'}),\n",
       "  frozenset({'23', '39', '59', '90'}),\n",
       "  frozenset({'34', '39', '59', '90'}),\n",
       "  frozenset({'23', '39', '85', '90'}),\n",
       "  frozenset({'3', '39', '85', '90'}),\n",
       "  frozenset({'34', '39', '85', '90'}),\n",
       "  frozenset({'39', '59', '85', '90'}),\n",
       "  frozenset({'23', '39', '90', '93'}),\n",
       "  frozenset({'34', '39', '90', '93'}),\n",
       "  frozenset({'39', '59', '90', '93'}),\n",
       "  frozenset({'39', '85', '90', '93'}),\n",
       "  frozenset({'2', '39', '59', '93'}),\n",
       "  frozenset({'2', '39', '85', '93'}),\n",
       "  frozenset({'23', '34', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '59'}),\n",
       "  frozenset({'23', '34', '36', '85'}),\n",
       "  frozenset({'23', '36', '59', '85'}),\n",
       "  frozenset({'23', '34', '36', '93'}),\n",
       "  frozenset({'23', '36', '59', '93'}),\n",
       "  frozenset({'23', '36', '85', '93'}),\n",
       "  frozenset({'34', '36', '59', '76'}),\n",
       "  frozenset({'1', '34', '36', '85'}),\n",
       "  frozenset({'3', '34', '36', '85'}),\n",
       "  frozenset({'34', '36', '59', '85'}),\n",
       "  frozenset({'34', '36', '76', '85'}),\n",
       "  frozenset({'1', '34', '36', '90'}),\n",
       "  frozenset({'23', '34', '36', '90'}),\n",
       "  frozenset({'3', '34', '36', '90'}),\n",
       "  frozenset({'34', '36', '59', '93'}),\n",
       "  frozenset({'34', '36', '85', '93'}),\n",
       "  frozenset({'34', '36', '52', '85'}),\n",
       "  frozenset({'34', '36', '52', '90'}),\n",
       "  frozenset({'23', '34', '59', '85'}),\n",
       "  frozenset({'23', '34', '59', '93'}),\n",
       "  frozenset({'23', '59', '85', '93'}),\n",
       "  frozenset({'34', '59', '76', '85'}),\n",
       "  frozenset({'34', '59', '85', '93'}),\n",
       "  frozenset({'36', '59', '76', '85'}),\n",
       "  frozenset({'36', '59', '85', '90'}),\n",
       "  frozenset({'36', '59', '85', '93'}),\n",
       "  frozenset({'36', '59', '90', '93'}),\n",
       "  frozenset({'23', '34', '63', '85'}),\n",
       "  frozenset({'23', '34', '63', '93'}),\n",
       "  frozenset({'23', '63', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '63'}),\n",
       "  frozenset({'23', '34', '59', '63'}),\n",
       "  frozenset({'34', '63', '76', '85'}),\n",
       "  frozenset({'23', '34', '63', '90'}),\n",
       "  frozenset({'34', '63', '85', '93'}),\n",
       "  frozenset({'23', '36', '59', '63'}),\n",
       "  frozenset({'34', '36', '59', '63'}),\n",
       "  frozenset({'23', '36', '63', '85'}),\n",
       "  frozenset({'34', '36', '63', '85'}),\n",
       "  frozenset({'36', '59', '63', '85'}),\n",
       "  frozenset({'23', '36', '63', '90'}),\n",
       "  frozenset({'34', '36', '63', '90'}),\n",
       "  frozenset({'36', '59', '63', '90'}),\n",
       "  frozenset({'36', '63', '85', '90'}),\n",
       "  frozenset({'23', '36', '63', '93'}),\n",
       "  frozenset({'34', '36', '63', '93'}),\n",
       "  frozenset({'36', '59', '63', '93'}),\n",
       "  frozenset({'36', '63', '85', '93'}),\n",
       "  frozenset({'36', '63', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '76'}),\n",
       "  frozenset({'23', '59', '63', '85'}),\n",
       "  frozenset({'34', '59', '63', '85'}),\n",
       "  frozenset({'59', '63', '76', '85'}),\n",
       "  frozenset({'23', '59', '63', '90'}),\n",
       "  frozenset({'34', '59', '63', '90'}),\n",
       "  frozenset({'59', '63', '85', '90'}),\n",
       "  frozenset({'23', '59', '63', '93'}),\n",
       "  frozenset({'34', '59', '63', '93'}),\n",
       "  frozenset({'59', '63', '85', '93'}),\n",
       "  frozenset({'59', '63', '90', '93'}),\n",
       "  frozenset({'34', '67', '76', '85'}),\n",
       "  frozenset({'34', '67', '85', '93'}),\n",
       "  frozenset({'34', '36', '59', '67'}),\n",
       "  frozenset({'34', '36', '67', '85'}),\n",
       "  frozenset({'36', '59', '67', '85'}),\n",
       "  frozenset({'34', '36', '67', '90'}),\n",
       "  frozenset({'34', '59', '63', '67'}),\n",
       "  frozenset({'34', '59', '67', '76'}),\n",
       "  frozenset({'34', '59', '67', '85'}),\n",
       "  frozenset({'59', '67', '76', '85'}),\n",
       "  frozenset({'34', '59', '67', '90'}),\n",
       "  frozenset({'34', '63', '67', '85'}),\n",
       "  frozenset({'59', '63', '67', '85'}),\n",
       "  frozenset({'34', '63', '67', '90'}),\n",
       "  frozenset({'63', '67', '85', '90'}),\n",
       "  frozenset({'34', '36', '76', '90'}),\n",
       "  frozenset({'34', '63', '76', '90'}),\n",
       "  frozenset({'34', '67', '76', '90'}),\n",
       "  frozenset({'34', '76', '85', '93'}),\n",
       "  frozenset({'1', '36', '85', '90'}),\n",
       "  frozenset({'23', '36', '85', '90'}),\n",
       "  frozenset({'3', '36', '85', '90'}),\n",
       "  frozenset({'34', '36', '85', '90'}),\n",
       "  frozenset({'36', '76', '85', '90'}),\n",
       "  frozenset({'34', '52', '85', '90'}),\n",
       "  frozenset({'36', '52', '85', '90'}),\n",
       "  frozenset({'23', '63', '85', '90'}),\n",
       "  frozenset({'34', '63', '85', '90'}),\n",
       "  frozenset({'63', '76', '85', '90'}),\n",
       "  frozenset({'34', '67', '85', '90'}),\n",
       "  frozenset({'36', '67', '85', '90'}),\n",
       "  frozenset({'59', '67', '85', '90'}),\n",
       "  frozenset({'67', '76', '85', '90'}),\n",
       "  frozenset({'23', '34', '85', '86'}),\n",
       "  frozenset({'23', '34', '86', '93'}),\n",
       "  frozenset({'23', '85', '86', '93'}),\n",
       "  frozenset({'1', '34', '36', '86'}),\n",
       "  frozenset({'23', '34', '36', '86'}),\n",
       "  frozenset({'3', '34', '36', '86'}),\n",
       "  frozenset({'23', '34', '59', '86'}),\n",
       "  frozenset({'23', '34', '63', '86'}),\n",
       "  frozenset({'34', '67', '76', '86'}),\n",
       "  frozenset({'1', '34', '85', '86'}),\n",
       "  frozenset({'3', '34', '85', '86'}),\n",
       "  frozenset({'34', '38', '85', '86'}),\n",
       "  frozenset({'34', '52', '85', '86'}),\n",
       "  frozenset({'34', '67', '85', '86'}),\n",
       "  frozenset({'34', '76', '85', '86'}),\n",
       "  frozenset({'1', '34', '86', '90'}),\n",
       "  frozenset({'23', '34', '86', '90'}),\n",
       "  frozenset({'3', '34', '86', '90'}),\n",
       "  frozenset({'34', '67', '86', '93'}),\n",
       "  frozenset({'34', '76', '86', '93'}),\n",
       "  frozenset({'34', '85', '86', '93'}),\n",
       "  frozenset({'34', '36', '52', '86'}),\n",
       "  frozenset({'23', '36', '59', '86'}),\n",
       "  frozenset({'34', '36', '59', '86'}),\n",
       "  frozenset({'23', '36', '63', '86'}),\n",
       "  frozenset({'34', '36', '63', '86'}),\n",
       "  frozenset({'34', '36', '67', '86'}),\n",
       "  frozenset({'36', '59', '67', '86'}),\n",
       "  frozenset({'34', '36', '76', '86'}),\n",
       "  frozenset({'36', '59', '76', '86'}),\n",
       "  frozenset({'1', '36', '85', '86'}),\n",
       "  frozenset({'23', '36', '85', '86'}),\n",
       "  frozenset({'3', '36', '85', '86'}),\n",
       "  frozenset({'34', '36', '85', '86'}),\n",
       "  frozenset({'36', '52', '85', '86'}),\n",
       "  frozenset({'36', '59', '85', '86'}),\n",
       "  frozenset({'36', '67', '85', '86'}),\n",
       "  frozenset({'36', '76', '85', '86'}),\n",
       "  frozenset({'1', '36', '86', '90'}),\n",
       "  frozenset({'23', '36', '86', '90'}),\n",
       "  frozenset({'3', '36', '86', '90'}),\n",
       "  frozenset({'34', '36', '86', '90'}),\n",
       "  frozenset({'23', '36', '86', '93'}),\n",
       "  frozenset({'34', '36', '86', '93'}),\n",
       "  frozenset({'36', '59', '86', '93'}),\n",
       "  frozenset({'36', '85', '86', '93'}),\n",
       "  frozenset({'34', '38', '86', '90'}),\n",
       "  frozenset({'34', '52', '86', '90'}),\n",
       "  frozenset({'36', '52', '86', '90'}),\n",
       "  frozenset({'23', '59', '63', '86'}),\n",
       "  frozenset({'34', '59', '63', '86'}),\n",
       "  frozenset({'36', '59', '63', '86'}),\n",
       "  frozenset({'34', '59', '67', '86'}),\n",
       "  frozenset({'34', '59', '76', '86'}),\n",
       "  frozenset({'59', '67', '76', '86'}),\n",
       "  frozenset({'23', '59', '85', '86'}),\n",
       "  frozenset({'34', '59', '85', '86'}),\n",
       "  frozenset({'59', '67', '85', '86'}),\n",
       "  frozenset({'59', '76', '85', '86'}),\n",
       "  frozenset({'23', '59', '86', '90'}),\n",
       "  frozenset({'34', '59', '86', '90'}),\n",
       "  frozenset({'36', '59', '86', '90'}),\n",
       "  frozenset({'23', '59', '86', '93'}),\n",
       "  frozenset({'34', '59', '86', '93'}),\n",
       "  frozenset({'59', '85', '86', '93'}),\n",
       "  frozenset({'34', '63', '67', '86'}),\n",
       "  frozenset({'59', '63', '67', '86'}),\n",
       "  frozenset({'34', '63', '76', '86'}),\n",
       "  frozenset({'59', '63', '76', '86'}),\n",
       "  frozenset({'23', '63', '85', '86'}),\n",
       "  frozenset({'34', '63', '85', '86'}),\n",
       "  frozenset({'36', '63', '85', '86'}),\n",
       "  frozenset({'59', '63', '85', '86'}),\n",
       "  frozenset({'63', '67', '85', '86'}),\n",
       "  frozenset({'63', '76', '85', '86'}),\n",
       "  frozenset({'23', '63', '86', '90'}),\n",
       "  frozenset({'34', '63', '86', '90'}),\n",
       "  frozenset({'36', '63', '86', '90'}),\n",
       "  frozenset({'59', '63', '86', '90'}),\n",
       "  frozenset({'63', '67', '86', '90'}),\n",
       "  frozenset({'63', '76', '86', '90'}),\n",
       "  frozenset({'63', '85', '86', '90'}),\n",
       "  frozenset({'23', '63', '86', '93'}),\n",
       "  frozenset({'34', '63', '86', '93'}),\n",
       "  frozenset({'36', '63', '86', '93'}),\n",
       "  frozenset({'59', '63', '86', '93'}),\n",
       "  frozenset({'63', '85', '86', '93'}),\n",
       "  frozenset({'63', '86', '90', '93'}),\n",
       "  frozenset({'34', '67', '86', '90'}),\n",
       "  frozenset({'36', '67', '86', '90'}),\n",
       "  frozenset({'59', '67', '86', '90'}),\n",
       "  frozenset({'67', '76', '85', '86'}),\n",
       "  frozenset({'34', '76', '86', '90'}),\n",
       "  frozenset({'36', '76', '86', '90'}),\n",
       "  frozenset({'59', '76', '86', '90'}),\n",
       "  frozenset({'67', '76', '86', '90'}),\n",
       "  frozenset({'1', '85', '86', '90'}),\n",
       "  frozenset({'23', '85', '86', '90'}),\n",
       "  frozenset({'3', '85', '86', '90'}),\n",
       "  frozenset({'34', '85', '86', '90'}),\n",
       "  frozenset({'36', '85', '86', '90'}),\n",
       "  frozenset({'38', '85', '86', '90'}),\n",
       "  frozenset({'52', '85', '86', '90'}),\n",
       "  frozenset({'59', '85', '86', '90'}),\n",
       "  frozenset({'67', '85', '86', '90'}),\n",
       "  frozenset({'76', '85', '86', '90'}),\n",
       "  frozenset({'67', '85', '86', '93'}),\n",
       "  frozenset({'76', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '59', '90'}),\n",
       "  frozenset({'23', '34', '85', '90'}),\n",
       "  frozenset({'23', '59', '85', '90'}),\n",
       "  frozenset({'23', '34', '90', '93'}),\n",
       "  frozenset({'23', '59', '90', '93'}),\n",
       "  frozenset({'23', '85', '90', '93'}),\n",
       "  frozenset({'34', '59', '76', '90'}),\n",
       "  frozenset({'1', '34', '85', '90'}),\n",
       "  frozenset({'3', '34', '85', '90'}),\n",
       "  frozenset({'34', '38', '85', '90'}),\n",
       "  frozenset({'34', '59', '85', '90'}),\n",
       "  frozenset({'34', '76', '85', '90'}),\n",
       "  frozenset({'34', '59', '90', '93'}),\n",
       "  frozenset({'34', '85', '90', '93'}),\n",
       "  frozenset({'23', '36', '90', '93'}),\n",
       "  frozenset({'34', '36', '90', '93'}),\n",
       "  frozenset({'36', '85', '90', '93'}),\n",
       "  frozenset({'23', '63', '90', '93'}),\n",
       "  frozenset({'34', '63', '90', '93'}),\n",
       "  frozenset({'63', '85', '90', '93'}),\n",
       "  frozenset({'59', '76', '85', '90'}),\n",
       "  frozenset({'59', '85', '90', '93'}),\n",
       "  frozenset({'23', '86', '90', '93'}),\n",
       "  frozenset({'34', '86', '90', '93'}),\n",
       "  frozenset({'36', '86', '90', '93'}),\n",
       "  frozenset({'59', '86', '90', '93'}),\n",
       "  frozenset({'85', '86', '90', '93'})],\n",
       " [frozenset({'1', '110', '24', '36', '86'}),\n",
       "  frozenset({'1', '110', '24', '36', '90'}),\n",
       "  frozenset({'1', '110', '24', '36', '85'}),\n",
       "  frozenset({'1', '110', '24', '34', '36'}),\n",
       "  frozenset({'1', '110', '24', '86', '90'}),\n",
       "  frozenset({'1', '110', '24', '85', '86'}),\n",
       "  frozenset({'1', '110', '24', '34', '86'}),\n",
       "  frozenset({'1', '110', '24', '85', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '85'}),\n",
       "  frozenset({'1', '24', '36', '86', '90'}),\n",
       "  frozenset({'1', '24', '36', '85', '86'}),\n",
       "  frozenset({'1', '24', '34', '36', '86'}),\n",
       "  frozenset({'1', '24', '36', '85', '90'}),\n",
       "  frozenset({'1', '24', '34', '36', '90'}),\n",
       "  frozenset({'1', '24', '34', '36', '85'}),\n",
       "  frozenset({'1', '24', '34', '85', '90'}),\n",
       "  frozenset({'1', '24', '85', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '85', '86'}),\n",
       "  frozenset({'110', '36', '53', '85', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '85'}),\n",
       "  frozenset({'110', '36', '53', '86', '90'}),\n",
       "  frozenset({'110', '36', '53', '85', '86'}),\n",
       "  frozenset({'110', '34', '36', '53', '86'}),\n",
       "  frozenset({'36', '53', '59', '86', '90'}),\n",
       "  frozenset({'36', '53', '59', '85', '86'}),\n",
       "  frozenset({'34', '36', '53', '59', '86'}),\n",
       "  frozenset({'34', '36', '53', '85', '86'}),\n",
       "  frozenset({'36', '53', '63', '85', '90'}),\n",
       "  frozenset({'34', '36', '53', '63', '90'}),\n",
       "  frozenset({'34', '36', '53', '63', '85'}),\n",
       "  frozenset({'34', '36', '56', '85', '86'}),\n",
       "  frozenset({'36', '39', '56', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '56', '86'}),\n",
       "  frozenset({'34', '39', '56', '85', '86'}),\n",
       "  frozenset({'116', '36', '85', '86', '90'}),\n",
       "  frozenset({'116', '34', '36', '86', '90'}),\n",
       "  frozenset({'116', '34', '36', '85', '86'}),\n",
       "  frozenset({'34', '36', '56', '85', '90'}),\n",
       "  frozenset({'116', '34', '36', '85', '90'}),\n",
       "  frozenset({'36', '53', '59', '85', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '90'}),\n",
       "  frozenset({'34', '36', '53', '85', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '85'}),\n",
       "  frozenset({'36', '39', '56', '86', '90'}),\n",
       "  frozenset({'39', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '39', '56', '86', '90'}),\n",
       "  frozenset({'36', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '56', '86', '90'}),\n",
       "  frozenset({'36', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '86', '90'}),\n",
       "  frozenset({'36', '53', '63', '86', '90'}),\n",
       "  frozenset({'36', '53', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '53', '63', '86'}),\n",
       "  frozenset({'110', '24', '85', '86', '90'}),\n",
       "  frozenset({'110', '24', '34', '86', '90'}),\n",
       "  frozenset({'110', '24', '36', '86', '90'}),\n",
       "  frozenset({'110', '24', '36', '85', '86'}),\n",
       "  frozenset({'110', '24', '34', '36', '86'}),\n",
       "  frozenset({'110', '24', '34', '85', '86'}),\n",
       "  frozenset({'110', '24', '34', '85', '90'}),\n",
       "  frozenset({'110', '24', '36', '85', '90'}),\n",
       "  frozenset({'110', '24', '34', '36', '90'}),\n",
       "  frozenset({'110', '24', '34', '36', '85'}),\n",
       "  frozenset({'110', '53', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '53', '86', '90'}),\n",
       "  frozenset({'110', '34', '53', '85', '86'}),\n",
       "  frozenset({'34', '56', '85', '86', '90'}),\n",
       "  frozenset({'116', '34', '56', '85', '90'}),\n",
       "  frozenset({'116', '34', '85', '86', '90'}),\n",
       "  frozenset({'116', '56', '85', '86', '90'}),\n",
       "  frozenset({'116', '34', '56', '86', '90'}),\n",
       "  frozenset({'116', '34', '56', '85', '86'}),\n",
       "  frozenset({'110', '34', '53', '85', '90'}),\n",
       "  frozenset({'34', '36', '6', '85', '90'}),\n",
       "  frozenset({'36', '6', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '6', '86', '90'}),\n",
       "  frozenset({'34', '36', '6', '85', '86'}),\n",
       "  frozenset({'34', '6', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '36', '85', '86'}),\n",
       "  frozenset({'24', '34', '36', '85', '90'}),\n",
       "  frozenset({'24', '36', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '36', '86', '90'}),\n",
       "  frozenset({'110', '34', '85', '86', '90'}),\n",
       "  frozenset({'110', '36', '85', '86', '90'}),\n",
       "  frozenset({'1', '110', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '36', '86', '90'}),\n",
       "  frozenset({'1', '110', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '34', '86', '90'}),\n",
       "  frozenset({'1', '110', '34', '85', '86'}),\n",
       "  frozenset({'1', '110', '34', '36', '86'}),\n",
       "  frozenset({'110', '34', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '34', '85', '90'}),\n",
       "  frozenset({'1', '110', '34', '36', '90'}),\n",
       "  frozenset({'1', '110', '34', '36', '85'}),\n",
       "  frozenset({'24', '53', '86', '90', '94'}),\n",
       "  frozenset({'24', '53', '85', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '90', '94'}),\n",
       "  frozenset({'34', '53', '85', '90', '94'}),\n",
       "  frozenset({'24', '53', '85', '86', '94'}),\n",
       "  frozenset({'53', '85', '86', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '86', '94'}),\n",
       "  frozenset({'34', '53', '86', '90', '94'}),\n",
       "  frozenset({'34', '53', '85', '86', '94'}),\n",
       "  frozenset({'24', '85', '86', '90', '94'}),\n",
       "  frozenset({'24', '34', '86', '90', '94'}),\n",
       "  frozenset({'34', '85', '86', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '85', '94'}),\n",
       "  frozenset({'24', '34', '85', '90', '94'}),\n",
       "  frozenset({'24', '34', '85', '86', '94'}),\n",
       "  frozenset({'34', '53', '76', '85', '90'}),\n",
       "  frozenset({'34', '53', '59', '85', '90'}),\n",
       "  frozenset({'34', '39', '53', '85', '90'}),\n",
       "  frozenset({'2', '34', '53', '85', '90'}),\n",
       "  frozenset({'2', '39', '53', '85', '90'}),\n",
       "  frozenset({'24', '53', '85', '86', '90'}),\n",
       "  frozenset({'53', '76', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '53', '86', '90'}),\n",
       "  frozenset({'34', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '76', '86', '90'}),\n",
       "  frozenset({'53', '67', '85', '86', '90'}),\n",
       "  frozenset({'53', '59', '85', '86', '90'}),\n",
       "  frozenset({'39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '76', '85', '86'}),\n",
       "  frozenset({'34', '53', '67', '86', '90'}),\n",
       "  frozenset({'34', '53', '67', '85', '86'}),\n",
       "  frozenset({'53', '63', '85', '86', '90'}),\n",
       "  frozenset({'53', '59', '63', '86', '90'}),\n",
       "  frozenset({'53', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '53', '63', '86', '90'}),\n",
       "  frozenset({'34', '53', '63', '85', '86'}),\n",
       "  frozenset({'34', '53', '59', '86', '90'}),\n",
       "  frozenset({'34', '53', '59', '85', '86'}),\n",
       "  frozenset({'34', '53', '59', '63', '86'}),\n",
       "  frozenset({'34', '39', '53', '86', '90'}),\n",
       "  frozenset({'34', '39', '53', '85', '86'}),\n",
       "  frozenset({'2', '34', '53', '86', '90'}),\n",
       "  frozenset({'2', '34', '53', '85', '86'}),\n",
       "  frozenset({'24', '34', '53', '85', '86'}),\n",
       "  frozenset({'2', '39', '53', '86', '90'}),\n",
       "  frozenset({'2', '39', '53', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '53', '86'}),\n",
       "  frozenset({'34', '53', '67', '85', '90'}),\n",
       "  frozenset({'34', '53', '63', '85', '90'}),\n",
       "  frozenset({'53', '59', '63', '85', '90'}),\n",
       "  frozenset({'34', '53', '59', '63', '90'}),\n",
       "  frozenset({'34', '53', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '39', '53', '85'}),\n",
       "  frozenset({'2', '34', '39', '53', '90'}),\n",
       "  frozenset({'2', '28', '39', '53', '85'}),\n",
       "  frozenset({'2', '28', '39', '53', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53'}),\n",
       "  frozenset({'28', '34', '39', '53', '85'}),\n",
       "  frozenset({'2', '28', '34', '53', '85'}),\n",
       "  frozenset({'2', '28', '39', '63', '85'}),\n",
       "  frozenset({'2', '28', '34', '39', '63'}),\n",
       "  frozenset({'2', '28', '34', '39', '85'}),\n",
       "  frozenset({'28', '39', '53', '85', '90'}),\n",
       "  frozenset({'28', '34', '39', '53', '90'}),\n",
       "  frozenset({'2', '28', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '53', '90'}),\n",
       "  frozenset({'28', '34', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '39', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '90'}),\n",
       "  frozenset({'28', '34', '39', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '85', '90'}),\n",
       "  frozenset({'28', '34', '85', '86', '90'}),\n",
       "  frozenset({'28', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '85', '86', '90'}),\n",
       "  frozenset({'28', '53', '85', '86', '90'}),\n",
       "  frozenset({'28', '34', '63', '85', '86'}),\n",
       "  frozenset({'28', '39', '63', '85', '86'}),\n",
       "  frozenset({'28', '34', '39', '63', '86'}),\n",
       "  frozenset({'2', '28', '63', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '63', '86'}),\n",
       "  frozenset({'28', '34', '59', '85', '86'}),\n",
       "  frozenset({'28', '39', '59', '85', '86'}),\n",
       "  frozenset({'28', '34', '39', '59', '86'}),\n",
       "  frozenset({'2', '28', '39', '59', '86'}),\n",
       "  frozenset({'2', '28', '59', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '59', '86'}),\n",
       "  frozenset({'28', '34', '39', '86', '90'}),\n",
       "  frozenset({'28', '34', '39', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '85', '86'}),\n",
       "  frozenset({'28', '34', '53', '86', '90'}),\n",
       "  frozenset({'28', '34', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '39', '86', '90'}),\n",
       "  frozenset({'2', '28', '39', '85', '86'}),\n",
       "  frozenset({'2', '28', '39', '63', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '86'}),\n",
       "  frozenset({'28', '39', '53', '86', '90'}),\n",
       "  frozenset({'28', '39', '53', '85', '86'}),\n",
       "  frozenset({'28', '34', '39', '53', '86'}),\n",
       "  frozenset({'2', '28', '39', '53', '86'}),\n",
       "  frozenset({'2', '28', '53', '86', '90'}),\n",
       "  frozenset({'2', '28', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '53', '86'}),\n",
       "  frozenset({'28', '34', '39', '63', '85'}),\n",
       "  frozenset({'2', '28', '34', '63', '85'}),\n",
       "  frozenset({'2', '28', '39', '59', '85'}),\n",
       "  frozenset({'2', '28', '34', '39', '59'}),\n",
       "  frozenset({'28', '39', '59', '63', '85'}),\n",
       "  frozenset({'28', '34', '39', '59', '85'}),\n",
       "  frozenset({'2', '28', '59', '85', '90'}),\n",
       "  frozenset({'2', '28', '59', '63', '85'}),\n",
       "  frozenset({'2', '28', '34', '59', '85'}),\n",
       "  frozenset({'24', '34', '85', '86', '90'}),\n",
       "  frozenset({'10', '34', '85', '86', '90'}),\n",
       "  frozenset({'10', '36', '85', '86', '90'}),\n",
       "  frozenset({'10', '34', '36', '86', '90'}),\n",
       "  frozenset({'10', '34', '36', '85', '86'}),\n",
       "  frozenset({'10', '34', '36', '85', '90'}),\n",
       "  frozenset({'39', '59', '85', '90', '93'}),\n",
       "  frozenset({'34', '39', '85', '90', '93'}),\n",
       "  frozenset({'23', '39', '85', '90', '93'}),\n",
       "  frozenset({'34', '39', '59', '90', '93'}),\n",
       "  frozenset({'34', '39', '59', '85', '90'}),\n",
       "  frozenset({'23', '34', '39', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '85', '90'}),\n",
       "  frozenset({'39', '85', '86', '90', '93'}),\n",
       "  frozenset({'39', '59', '86', '90', '93'}),\n",
       "  frozenset({'34', '39', '86', '90', '93'}),\n",
       "  frozenset({'34', '39', '85', '86', '90'}),\n",
       "  frozenset({'23', '39', '86', '90', '93'}),\n",
       "  frozenset({'39', '59', '85', '86', '93'}),\n",
       "  frozenset({'39', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '39', '85', '86', '90'}),\n",
       "  frozenset({'34', '39', '76', '85', '86'}),\n",
       "  frozenset({'2', '39', '76', '85', '86'}),\n",
       "  frozenset({'34', '39', '67', '85', '86'}),\n",
       "  frozenset({'2', '39', '67', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '67', '86'}),\n",
       "  frozenset({'2', '39', '63', '86', '90'}),\n",
       "  frozenset({'2', '39', '63', '85', '86'}),\n",
       "  frozenset({'39', '63', '85', '86', '93'}),\n",
       "  frozenset({'39', '63', '85', '86', '90'}),\n",
       "  frozenset({'39', '59', '63', '86', '93'}),\n",
       "  frozenset({'39', '59', '63', '86', '90'}),\n",
       "  frozenset({'39', '59', '63', '85', '86'}),\n",
       "  frozenset({'36', '39', '63', '86', '93'}),\n",
       "  frozenset({'36', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '39', '63', '86', '93'}),\n",
       "  frozenset({'34', '39', '63', '86', '90'}),\n",
       "  frozenset({'34', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '63', '86'}),\n",
       "  frozenset({'23', '39', '63', '86', '93'}),\n",
       "  frozenset({'23', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '39', '59', '86', '93'}),\n",
       "  frozenset({'34', '39', '59', '86', '90'}),\n",
       "  frozenset({'34', '39', '59', '85', '86'}),\n",
       "  frozenset({'34', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '39', '59', '86', '93'}),\n",
       "  frozenset({'23', '39', '59', '86', '90'}),\n",
       "  frozenset({'23', '39', '59', '85', '86'}),\n",
       "  frozenset({'23', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '34', '39', '59', '86'}),\n",
       "  frozenset({'2', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '39', '59', '86', '90'}),\n",
       "  frozenset({'2', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '39', '59', '86'}),\n",
       "  frozenset({'2', '23', '39', '59', '86'}),\n",
       "  frozenset({'34', '39', '52', '85', '86'}),\n",
       "  frozenset({'2', '36', '39', '86', '93'}),\n",
       "  frozenset({'2', '36', '39', '85', '86'}),\n",
       "  frozenset({'2', '36', '39', '63', '86'}),\n",
       "  frozenset({'36', '39', '86', '90', '93'}),\n",
       "  frozenset({'36', '39', '85', '86', '90'}),\n",
       "  frozenset({'36', '39', '85', '86', '93'}),\n",
       "  frozenset({'36', '39', '59', '86', '93'}),\n",
       "  frozenset({'36', '39', '59', '86', '90'}),\n",
       "  frozenset({'36', '39', '59', '85', '86'}),\n",
       "  frozenset({'36', '39', '59', '63', '86'}),\n",
       "  frozenset({'34', '36', '39', '59', '86'}),\n",
       "  frozenset({'23', '36', '39', '59', '86'}),\n",
       "  frozenset({'2', '36', '39', '59', '86'}),\n",
       "  frozenset({'34', '36', '39', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '86', '93'}),\n",
       "  frozenset({'34', '36', '39', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '86', '90'}),\n",
       "  frozenset({'23', '36', '39', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '63', '86'}),\n",
       "  frozenset({'3', '34', '39', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '86', '90'}),\n",
       "  frozenset({'23', '34', '39', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '63', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '86'}),\n",
       "  frozenset({'2', '34', '39', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '76', '86'}),\n",
       "  frozenset({'2', '34', '39', '63', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '86'}),\n",
       "  frozenset({'2', '23', '39', '86', '93'}),\n",
       "  frozenset({'2', '23', '39', '85', '86'}),\n",
       "  frozenset({'2', '23', '39', '63', '86'}),\n",
       "  frozenset({'2', '23', '36', '39', '86'}),\n",
       "  frozenset({'2', '23', '34', '39', '86'}),\n",
       "  frozenset({'2', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '34', '39', '67', '85'}),\n",
       "  frozenset({'39', '63', '85', '90', '93'}),\n",
       "  frozenset({'39', '59', '63', '90', '93'}),\n",
       "  frozenset({'36', '39', '63', '90', '93'}),\n",
       "  frozenset({'34', '39', '63', '85', '90'}),\n",
       "  frozenset({'39', '59', '63', '85', '93'}),\n",
       "  frozenset({'39', '59', '63', '85', '90'}),\n",
       "  frozenset({'36', '39', '63', '85', '93'}),\n",
       "  frozenset({'36', '39', '63', '85', '90'}),\n",
       "  frozenset({'34', '39', '63', '85', '93'}),\n",
       "  frozenset({'23', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '39', '63', '85', '90'}),\n",
       "  frozenset({'36', '39', '59', '63', '93'}),\n",
       "  frozenset({'36', '39', '59', '63', '90'}),\n",
       "  frozenset({'36', '39', '59', '63', '85'}),\n",
       "  frozenset({'34', '39', '59', '63', '93'}),\n",
       "  frozenset({'34', '39', '59', '63', '90'}),\n",
       "  frozenset({'34', '39', '59', '63', '85'}),\n",
       "  frozenset({'34', '36', '39', '59', '63'}),\n",
       "  frozenset({'2', '39', '59', '63', '93'}),\n",
       "  frozenset({'2', '39', '59', '63', '85'}),\n",
       "  frozenset({'34', '36', '39', '63', '93'}),\n",
       "  frozenset({'34', '36', '39', '63', '85'}),\n",
       "  frozenset({'23', '36', '39', '63', '93'}),\n",
       "  frozenset({'23', '36', '39', '63', '85'}),\n",
       "  frozenset({'2', '36', '39', '63', '93'}),\n",
       "  frozenset({'2', '36', '39', '63', '85'}),\n",
       "  frozenset({'23', '34', '39', '63', '93'}),\n",
       "  frozenset({'23', '34', '39', '63', '85'}),\n",
       "  frozenset({'23', '34', '36', '39', '63'}),\n",
       "  frozenset({'2', '34', '39', '63', '90'}),\n",
       "  frozenset({'2', '34', '39', '63', '85'}),\n",
       "  frozenset({'2', '34', '36', '39', '63'}),\n",
       "  frozenset({'36', '39', '85', '90', '93'}),\n",
       "  frozenset({'36', '39', '59', '90', '93'}),\n",
       "  frozenset({'36', '39', '59', '85', '90'}),\n",
       "  frozenset({'34', '36', '39', '59', '90'}),\n",
       "  frozenset({'34', '36', '39', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '85', '90'}),\n",
       "  frozenset({'23', '36', '39', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '90'}),\n",
       "  frozenset({'36', '39', '59', '85', '93'}),\n",
       "  frozenset({'34', '36', '39', '85', '93'}),\n",
       "  frozenset({'23', '36', '39', '85', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '85'}),\n",
       "  frozenset({'23', '36', '39', '59', '90'}),\n",
       "  frozenset({'23', '36', '39', '59', '63'}),\n",
       "  frozenset({'23', '34', '36', '39', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '85'}),\n",
       "  frozenset({'2', '34', '39', '85', '93'}),\n",
       "  frozenset({'2', '34', '39', '76', '85'}),\n",
       "  frozenset({'2', '34', '39', '59', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '85'}),\n",
       "  frozenset({'2', '34', '39', '59', '63'}),\n",
       "  frozenset({'34', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '39', '63', '85'}),\n",
       "  frozenset({'2', '23', '39', '85', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '63'}),\n",
       "  frozenset({'2', '23', '39', '59', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '85'}),\n",
       "  frozenset({'2', '23', '34', '39', '63'}),\n",
       "  frozenset({'2', '23', '34', '39', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '85'}),\n",
       "  frozenset({'2', '23', '34', '39', '59'}),\n",
       "  frozenset({'23', '39', '59', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '93'}),\n",
       "  frozenset({'23', '39', '59', '85', '90'}),\n",
       "  frozenset({'23', '39', '59', '63', '85'}),\n",
       "  frozenset({'23', '36', '39', '59', '85'}),\n",
       "  frozenset({'23', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '39', '85', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '90'}),\n",
       "  frozenset({'23', '34', '39', '59', '63'}),\n",
       "  frozenset({'23', '34', '36', '39', '59'}),\n",
       "  frozenset({'23', '34', '39', '59', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85'}),\n",
       "  frozenset({'2', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '85', '90', '93'}),\n",
       "  frozenset({'2', '39', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '85', '90'}),\n",
       "  frozenset({'2', '39', '59', '90', '93'}),\n",
       "  frozenset({'2', '39', '59', '85', '90'}),\n",
       "  frozenset({'2', '39', '59', '63', '90'}),\n",
       "  frozenset({'2', '34', '39', '59', '90'}),\n",
       "  frozenset({'2', '34', '39', '85', '90'}),\n",
       "  frozenset({'2', '23', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '85', '90'}),\n",
       "  frozenset({'2', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '76', '85', '86'}),\n",
       "  frozenset({'2', '34', '67', '85', '86'}),\n",
       "  frozenset({'2', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '59', '63', '86', '90'}),\n",
       "  frozenset({'2', '36', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '63', '86', '93'}),\n",
       "  frozenset({'2', '34', '63', '86', '90'}),\n",
       "  frozenset({'2', '34', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '63', '86'}),\n",
       "  frozenset({'2', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '59', '63', '86', '93'}),\n",
       "  frozenset({'2', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '59', '86', '90'}),\n",
       "  frozenset({'2', '34', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '59', '86', '93'}),\n",
       "  frozenset({'2', '34', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '59', '86', '90'}),\n",
       "  frozenset({'2', '23', '59', '63', '86'}),\n",
       "  frozenset({'2', '23', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '59', '86'}),\n",
       "  frozenset({'2', '36', '86', '90', '93'}),\n",
       "  frozenset({'2', '36', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '85', '86', '93'}),\n",
       "  frozenset({'2', '36', '59', '86', '90'}),\n",
       "  frozenset({'2', '36', '59', '63', '86'}),\n",
       "  frozenset({'2', '36', '59', '86', '93'}),\n",
       "  frozenset({'2', '36', '59', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '59', '86'}),\n",
       "  frozenset({'2', '23', '36', '59', '86'}),\n",
       "  frozenset({'2', '34', '36', '86', '90'}),\n",
       "  frozenset({'2', '34', '36', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '63', '86'}),\n",
       "  frozenset({'2', '23', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '86', '93'}),\n",
       "  frozenset({'2', '23', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '85', '86'}),\n",
       "  frozenset({'2', '23', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '63', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '86'}),\n",
       "  frozenset({'2', '23', '34', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '85', '86'}),\n",
       "  frozenset({'2', '63', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '63', '85', '90'}),\n",
       "  frozenset({'2', '34', '63', '85', '93'}),\n",
       "  frozenset({'2', '59', '63', '90', '93'}),\n",
       "  frozenset({'2', '59', '63', '85', '93'}),\n",
       "  frozenset({'2', '59', '63', '85', '90'}),\n",
       "  frozenset({'2', '34', '59', '63', '93'}),\n",
       "  frozenset({'2', '34', '59', '63', '90'}),\n",
       "  frozenset({'2', '34', '59', '63', '85'}),\n",
       "  frozenset({'2', '36', '63', '90', '93'}),\n",
       "  frozenset({'2', '36', '63', '85', '93'}),\n",
       "  frozenset({'2', '36', '63', '85', '90'}),\n",
       "  frozenset({'2', '36', '59', '63', '93'}),\n",
       "  frozenset({'2', '36', '59', '63', '90'}),\n",
       "  frozenset({'2', '36', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '36', '59', '63'}),\n",
       "  frozenset({'2', '34', '36', '63', '85'}),\n",
       "  frozenset({'2', '23', '36', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '63'}),\n",
       "  frozenset({'2', '23', '34', '63', '85'}),\n",
       "  frozenset({'2', '34', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '59', '90', '93'}),\n",
       "  frozenset({'2', '23', '59', '85', '90'}),\n",
       "  frozenset({'2', '23', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '90'}),\n",
       "  frozenset({'2', '23', '34', '59', '63'}),\n",
       "  frozenset({'2', '23', '34', '59', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85'}),\n",
       "  frozenset({'2', '36', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '85', '90'}),\n",
       "  frozenset({'2', '36', '59', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '85', '93'}),\n",
       "  frozenset({'2', '36', '39', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '85'}),\n",
       "  frozenset({'2', '36', '39', '59', '93'}),\n",
       "  frozenset({'2', '36', '39', '59', '85'}),\n",
       "  frozenset({'2', '36', '39', '59', '63'}),\n",
       "  frozenset({'2', '34', '36', '39', '59'}),\n",
       "  frozenset({'2', '36', '39', '59', '90'}),\n",
       "  frozenset({'2', '34', '36', '39', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '85'}),\n",
       "  frozenset({'2', '23', '36', '85', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '63'}),\n",
       "  frozenset({'2', '23', '36', '59', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '59'}),\n",
       "  frozenset({'2', '23', '34', '36', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '85'}),\n",
       "  frozenset({'2', '23', '34', '85', '93'}),\n",
       "  frozenset({'34', '59', '85', '90', '93'}),\n",
       "  frozenset({'34', '59', '76', '85', '90'}),\n",
       "  frozenset({'23', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '85', '90'}),\n",
       "  frozenset({'59', '85', '86', '90', '93'}),\n",
       "  frozenset({'36', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '85', '86', '90', '93'}),\n",
       "  frozenset({'67', '76', '85', '86', '90'}),\n",
       "  frozenset({'59', '76', '85', '86', '90'}),\n",
       "  frozenset({'36', '76', '85', '86', '90'}),\n",
       "  frozenset({'34', '76', '85', '86', '90'}),\n",
       "  frozenset({'34', '67', '85', '86', '90'}),\n",
       "  frozenset({'34', '67', '76', '86', '90'}),\n",
       "  frozenset({'63', '85', '86', '90', '93'}),\n",
       "  frozenset({'63', '76', '85', '86', '90'}),\n",
       "  frozenset({'59', '63', '86', '90', '93'}),\n",
       "  frozenset({'36', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '63', '76', '86', '90'}),\n",
       "  frozenset({'23', '63', '86', '90', '93'}),\n",
       "  frozenset({'63', '67', '85', '86', '90'}),\n",
       "  frozenset({'59', '63', '85', '86', '93'}),\n",
       "  frozenset({'59', '63', '85', '86', '90'}),\n",
       "  frozenset({'36', '63', '85', '86', '93'}),\n",
       "  frozenset({'36', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '63', '85', '86', '90'}),\n",
       "  frozenset({'59', '63', '76', '85', '86'}),\n",
       "  frozenset({'34', '63', '76', '85', '86'}),\n",
       "  frozenset({'34', '63', '67', '86', '90'}),\n",
       "  frozenset({'34', '63', '67', '85', '86'}),\n",
       "  frozenset({'34', '59', '86', '90', '93'}),\n",
       "  frozenset({'34', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '59', '76', '86', '90'}),\n",
       "  frozenset({'23', '59', '86', '90', '93'}),\n",
       "  frozenset({'59', '67', '85', '86', '90'}),\n",
       "  frozenset({'59', '63', '67', '85', '86'}),\n",
       "  frozenset({'34', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '59', '85', '86', '90'}),\n",
       "  frozenset({'59', '67', '76', '85', '86'}),\n",
       "  frozenset({'34', '59', '76', '85', '86'}),\n",
       "  frozenset({'34', '59', '67', '86', '90'}),\n",
       "  frozenset({'34', '59', '63', '67', '86'}),\n",
       "  frozenset({'34', '59', '67', '85', '86'}),\n",
       "  frozenset({'34', '59', '67', '76', '86'}),\n",
       "  frozenset({'36', '59', '63', '86', '93'}),\n",
       "  frozenset({'36', '59', '63', '86', '90'}),\n",
       "  frozenset({'36', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '59', '63', '86', '93'}),\n",
       "  frozenset({'34', '59', '63', '86', '90'}),\n",
       "  frozenset({'34', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '59', '63', '76', '86'}),\n",
       "  frozenset({'34', '36', '59', '63', '86'}),\n",
       "  frozenset({'23', '59', '63', '86', '93'}),\n",
       "  frozenset({'23', '59', '63', '86', '90'}),\n",
       "  frozenset({'23', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '52', '85', '86', '90'}),\n",
       "  frozenset({'34', '38', '85', '86', '90'}),\n",
       "  frozenset({'36', '59', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '76', '86', '90'}),\n",
       "  frozenset({'3', '36', '85', '86', '90'}),\n",
       "  frozenset({'3', '34', '36', '86', '90'}),\n",
       "  frozenset({'23', '36', '86', '90', '93'}),\n",
       "  frozenset({'36', '67', '85', '86', '90'}),\n",
       "  frozenset({'36', '59', '85', '86', '90'}),\n",
       "  frozenset({'36', '59', '85', '86', '93'}),\n",
       "  frozenset({'36', '52', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '85', '86', '90'}),\n",
       "  frozenset({'1', '36', '85', '86', '90'}),\n",
       "  frozenset({'36', '59', '76', '85', '86'}),\n",
       "  frozenset({'34', '36', '76', '85', '86'}),\n",
       "  frozenset({'36', '59', '67', '85', '86'}),\n",
       "  frozenset({'34', '36', '59', '67', '86'}),\n",
       "  frozenset({'34', '36', '67', '86', '90'}),\n",
       "  frozenset({'34', '36', '67', '85', '86'}),\n",
       "  frozenset({'34', '36', '63', '86', '93'}),\n",
       "  frozenset({'34', '36', '63', '86', '90'}),\n",
       "  frozenset({'34', '36', '63', '85', '86'}),\n",
       "  frozenset({'23', '36', '63', '86', '93'}),\n",
       "  frozenset({'23', '36', '63', '86', '90'}),\n",
       "  frozenset({'23', '36', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '59', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '86', '93'}),\n",
       "  frozenset({'34', '36', '59', '85', '86'}),\n",
       "  frozenset({'34', '36', '59', '76', '86'}),\n",
       "  frozenset({'23', '36', '59', '86', '93'}),\n",
       "  frozenset({'23', '36', '59', '86', '90'}),\n",
       "  frozenset({'23', '36', '59', '85', '86'}),\n",
       "  frozenset({'23', '36', '59', '63', '86'}),\n",
       "  frozenset({'34', '36', '52', '86', '90'}),\n",
       "  frozenset({'34', '36', '52', '85', '86'}),\n",
       "  frozenset({'3', '34', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '85', '86', '90'}),\n",
       "  frozenset({'1', '34', '85', '86', '90'}),\n",
       "  frozenset({'34', '76', '85', '86', '93'}),\n",
       "  frozenset({'34', '67', '85', '86', '93'}),\n",
       "  frozenset({'34', '67', '76', '85', '86'}),\n",
       "  frozenset({'23', '34', '63', '86', '93'}),\n",
       "  frozenset({'23', '34', '63', '86', '90'}),\n",
       "  frozenset({'23', '34', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '63', '86'}),\n",
       "  frozenset({'23', '34', '59', '86', '93'}),\n",
       "  frozenset({'23', '34', '59', '86', '90'}),\n",
       "  frozenset({'23', '34', '59', '85', '86'}),\n",
       "  frozenset({'23', '34', '59', '63', '86'}),\n",
       "  frozenset({'23', '34', '36', '59', '86'}),\n",
       "  frozenset({'3', '34', '36', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '85', '86'}),\n",
       "  frozenset({'1', '34', '36', '86', '90'}),\n",
       "  frozenset({'1', '34', '36', '85', '86'}),\n",
       "  frozenset({'23', '34', '85', '86', '93'}),\n",
       "  frozenset({'34', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '63', '85', '90', '93'}),\n",
       "  frozenset({'34', '36', '85', '90', '93'}),\n",
       "  frozenset({'23', '36', '85', '90', '93'}),\n",
       "  frozenset({'34', '67', '76', '85', '90'}),\n",
       "  frozenset({'34', '63', '76', '85', '90'}),\n",
       "  frozenset({'34', '36', '76', '85', '90'}),\n",
       "  frozenset({'34', '63', '67', '85', '90'}),\n",
       "  frozenset({'34', '59', '67', '85', '90'}),\n",
       "  frozenset({'34', '59', '67', '76', '85'}),\n",
       "  frozenset({'34', '59', '63', '67', '85'}),\n",
       "  frozenset({'34', '36', '67', '85', '90'}),\n",
       "  frozenset({'34', '36', '59', '67', '85'}),\n",
       "  frozenset({'59', '63', '85', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '85', '90'}),\n",
       "  frozenset({'23', '59', '63', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '85', '93'}),\n",
       "  frozenset({'23', '59', '63', '85', '93'}),\n",
       "  frozenset({'23', '59', '63', '85', '90'}),\n",
       "  frozenset({'34', '59', '63', '76', '85'}),\n",
       "  frozenset({'36', '63', '85', '90', '93'}),\n",
       "  frozenset({'36', '59', '63', '90', '93'}),\n",
       "  frozenset({'34', '36', '63', '90', '93'}),\n",
       "  frozenset({'23', '36', '63', '90', '93'}),\n",
       "  frozenset({'36', '59', '63', '85', '93'}),\n",
       "  frozenset({'36', '59', '63', '85', '90'}),\n",
       "  frozenset({'34', '36', '63', '85', '93'}),\n",
       "  frozenset({'34', '36', '63', '85', '90'}),\n",
       "  frozenset({'23', '36', '63', '85', '93'}),\n",
       "  frozenset({'23', '36', '63', '85', '90'}),\n",
       "  frozenset({'34', '36', '59', '63', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '90'}),\n",
       "  frozenset({'34', '36', '59', '63', '85'}),\n",
       "  frozenset({'23', '36', '59', '63', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '90'}),\n",
       "  frozenset({'23', '36', '59', '63', '85'}),\n",
       "  frozenset({'23', '34', '63', '90', '93'}),\n",
       "  frozenset({'23', '34', '63', '85', '90'}),\n",
       "  frozenset({'23', '34', '59', '63', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '90'}),\n",
       "  frozenset({'23', '34', '59', '63', '85'}),\n",
       "  frozenset({'23', '34', '36', '59', '63'}),\n",
       "  frozenset({'23', '34', '36', '63', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '90'}),\n",
       "  frozenset({'23', '34', '36', '63', '85'}),\n",
       "  frozenset({'23', '34', '63', '85', '93'}),\n",
       "  frozenset({'36', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '85', '93'}),\n",
       "  frozenset({'34', '36', '52', '85', '90'}),\n",
       "  frozenset({'3', '34', '36', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '85', '90'}),\n",
       "  frozenset({'1', '34', '36', '85', '90'}),\n",
       "  frozenset({'34', '36', '59', '85', '93'}),\n",
       "  frozenset({'34', '36', '59', '76', '85'}),\n",
       "  frozenset({'23', '36', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '85'})],\n",
       " [frozenset({'1', '110', '24', '34', '36', '86'}),\n",
       "  frozenset({'1', '110', '24', '34', '36', '85'}),\n",
       "  frozenset({'1', '110', '24', '34', '36', '90'}),\n",
       "  frozenset({'1', '110', '24', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '24', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '24', '36', '86', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '85', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '85', '86'}),\n",
       "  frozenset({'1', '110', '24', '34', '86', '90'}),\n",
       "  frozenset({'1', '110', '24', '85', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '85', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '36', '85', '90'}),\n",
       "  frozenset({'1', '24', '34', '36', '85', '86'}),\n",
       "  frozenset({'1', '24', '34', '36', '86', '90'}),\n",
       "  frozenset({'1', '24', '36', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '85', '86'}),\n",
       "  frozenset({'110', '36', '53', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '85', '90'}),\n",
       "  frozenset({'34', '36', '53', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '53', '63', '86', '90'}),\n",
       "  frozenset({'36', '53', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '85', '90'}),\n",
       "  frozenset({'116', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'34', '39', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '56', '86', '90'}),\n",
       "  frozenset({'36', '39', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '56', '85', '86'}),\n",
       "  frozenset({'34', '36', '53', '63', '85', '90'}),\n",
       "  frozenset({'34', '36', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '85', '86'}),\n",
       "  frozenset({'36', '53', '59', '85', '86', '90'}),\n",
       "  frozenset({'110', '24', '34', '36', '85', '90'}),\n",
       "  frozenset({'110', '24', '34', '36', '85', '86'}),\n",
       "  frozenset({'110', '24', '34', '36', '86', '90'}),\n",
       "  frozenset({'110', '24', '36', '85', '86', '90'}),\n",
       "  frozenset({'110', '24', '34', '85', '86', '90'}),\n",
       "  frozenset({'116', '34', '56', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '6', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'1', '110', '34', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '34', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '34', '36', '86', '90'}),\n",
       "  frozenset({'1', '110', '34', '85', '86', '90'}),\n",
       "  frozenset({'1', '110', '36', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '59', '85'}),\n",
       "  frozenset({'2', '28', '53', '85', '86', '90'}),\n",
       "  frozenset({'28', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '59', '86'}),\n",
       "  frozenset({'2', '28', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '28', '39', '85', '86', '90'}),\n",
       "  frozenset({'28', '34', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '85', '86', '90'}),\n",
       "  frozenset({'28', '34', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '59', '85', '86'}),\n",
       "  frozenset({'2', '28', '39', '59', '85', '86'}),\n",
       "  frozenset({'28', '34', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '63', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '63', '86'}),\n",
       "  frozenset({'28', '34', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '63', '85'}),\n",
       "  frozenset({'2', '28', '34', '53', '85', '90'}),\n",
       "  frozenset({'28', '34', '39', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '39', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '85'}),\n",
       "  frozenset({'2', '34', '39', '53', '85', '90'}),\n",
       "  frozenset({'34', '53', '59', '63', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '86'}),\n",
       "  frozenset({'2', '28', '39', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '39', '53', '86', '90'}),\n",
       "  frozenset({'2', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '53', '86', '90'}),\n",
       "  frozenset({'2', '34', '53', '85', '86', '90'}),\n",
       "  frozenset({'28', '34', '39', '53', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '53', '85', '86'}),\n",
       "  frozenset({'28', '34', '39', '53', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '53', '86', '90'}),\n",
       "  frozenset({'34', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '53', '59', '63', '86', '90'}),\n",
       "  frozenset({'34', '53', '63', '85', '86', '90'}),\n",
       "  frozenset({'53', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '67', '85', '86', '90'}),\n",
       "  frozenset({'34', '53', '76', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '53', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '85', '86', '90', '94'}),\n",
       "  frozenset({'34', '53', '85', '86', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '85', '86', '94'}),\n",
       "  frozenset({'24', '34', '53', '86', '90', '94'}),\n",
       "  frozenset({'24', '34', '53', '85', '90', '94'}),\n",
       "  frozenset({'24', '53', '85', '86', '90', '94'}),\n",
       "  frozenset({'10', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '36', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '36', '39', '85', '93'}),\n",
       "  frozenset({'2', '36', '39', '59', '85', '90'}),\n",
       "  frozenset({'2', '36', '39', '59', '90', '93'}),\n",
       "  frozenset({'2', '36', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '85'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '90'}),\n",
       "  frozenset({'2', '23', '34', '59', '90', '93'}),\n",
       "  frozenset({'2', '23', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '63'}),\n",
       "  frozenset({'2', '34', '36', '59', '63', '85'}),\n",
       "  frozenset({'2', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '36', '59', '63', '85', '90'}),\n",
       "  frozenset({'2', '36', '39', '59', '63', '93'}),\n",
       "  frozenset({'2', '36', '59', '63', '85', '93'}),\n",
       "  frozenset({'2', '36', '59', '63', '90', '93'}),\n",
       "  frozenset({'2', '36', '63', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '63', '85', '90'}),\n",
       "  frozenset({'2', '34', '59', '63', '85', '93'}),\n",
       "  frozenset({'2', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '36', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '86'}),\n",
       "  frozenset({'2', '34', '36', '59', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '59', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '86', '90'}),\n",
       "  frozenset({'2', '23', '36', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '59', '86', '93'}),\n",
       "  frozenset({'2', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '63', '86'}),\n",
       "  frozenset({'2', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '36', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '36', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '59', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '59', '63', '86', '90'}),\n",
       "  frozenset({'2', '34', '59', '63', '86', '93'}),\n",
       "  frozenset({'2', '34', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '63', '86'}),\n",
       "  frozenset({'2', '34', '36', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '85', '90', '93'}),\n",
       "  frozenset({'2', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '90'}),\n",
       "  frozenset({'23', '34', '39', '59', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '85'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '63'}),\n",
       "  frozenset({'2', '23', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '39', '59', '85', '90'}),\n",
       "  frozenset({'2', '34', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '90'}),\n",
       "  frozenset({'23', '36', '39', '59', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '85', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '85', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '90'}),\n",
       "  frozenset({'34', '36', '39', '59', '90', '93'}),\n",
       "  frozenset({'36', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '39', '63', '85', '90'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '63'}),\n",
       "  frozenset({'23', '34', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '39', '63', '85'}),\n",
       "  frozenset({'23', '34', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '36', '39', '63', '85', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'23', '36', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '63', '85'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '85'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '93'}),\n",
       "  frozenset({'34', '36', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '39', '59', '63', '85', '90'}),\n",
       "  frozenset({'2', '39', '59', '63', '85', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '63'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '63'}),\n",
       "  frozenset({'34', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'34', '39', '59', '63', '85', '90'}),\n",
       "  frozenset({'34', '39', '59', '63', '85', '93'}),\n",
       "  frozenset({'36', '39', '59', '63', '85', '90'}),\n",
       "  frozenset({'36', '39', '59', '63', '85', '93'}),\n",
       "  frozenset({'36', '39', '59', '63', '90', '93'}),\n",
       "  frozenset({'36', '39', '63', '85', '90', '93'}),\n",
       "  frozenset({'39', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '76', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '86'}),\n",
       "  frozenset({'2', '23', '34', '39', '63', '86'}),\n",
       "  frozenset({'2', '23', '34', '39', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '39', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '36', '39', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '86', '93'}),\n",
       "  frozenset({'34', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '86'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '86', '90'}),\n",
       "  frozenset({'23', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '59', '86', '90'}),\n",
       "  frozenset({'36', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'36', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'36', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '63', '86'}),\n",
       "  frozenset({'2', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '59', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '86'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '59', '86', '90'}),\n",
       "  frozenset({'23', '34', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'23', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '34', '39', '59', '63', '86'}),\n",
       "  frozenset({'34', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'34', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '39', '63', '85', '86'}),\n",
       "  frozenset({'23', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '86'}),\n",
       "  frozenset({'34', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '63', '86', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '63', '86'}),\n",
       "  frozenset({'2', '34', '39', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '63', '86', '90'}),\n",
       "  frozenset({'34', '39', '59', '63', '86', '90'}),\n",
       "  frozenset({'34', '39', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '39', '63', '86', '93'}),\n",
       "  frozenset({'34', '39', '59', '63', '86', '93'}),\n",
       "  frozenset({'34', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'23', '36', '39', '63', '86', '93'}),\n",
       "  frozenset({'36', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'39', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'39', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '39', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '67', '85', '86'}),\n",
       "  frozenset({'23', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '85', '90', '93'}),\n",
       "  frozenset({'34', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '90'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '90', '93'}),\n",
       "  frozenset({'23', '34', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '90'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '90'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '90', '93'}),\n",
       "  frozenset({'23', '36', '63', '85', '90', '93'}),\n",
       "  frozenset({'34', '36', '63', '85', '90', '93'}),\n",
       "  frozenset({'36', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'1', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '52', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '59', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '85', '86'}),\n",
       "  frozenset({'34', '36', '59', '76', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '59', '86', '93'}),\n",
       "  frozenset({'34', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '63', '86', '90'}),\n",
       "  frozenset({'34', '36', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '63', '86', '93'}),\n",
       "  frozenset({'34', '36', '63', '85', '86', '93'}),\n",
       "  frozenset({'34', '36', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '67', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '67', '85', '86'}),\n",
       "  frozenset({'23', '36', '85', '86', '90', '93'}),\n",
       "  frozenset({'3', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '76', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '85', '86', '90', '93'}),\n",
       "  frozenset({'36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '86'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '59', '63', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '63', '86', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '59', '63', '76', '85', '86'}),\n",
       "  frozenset({'23', '34', '59', '63', '86', '90'}),\n",
       "  frozenset({'34', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '59', '63', '86', '93'}),\n",
       "  frozenset({'34', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'34', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '36', '59', '63', '86', '90'}),\n",
       "  frozenset({'36', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '59', '63', '86', '93'}),\n",
       "  frozenset({'36', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'36', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '59', '67', '76', '85', '86'}),\n",
       "  frozenset({'34', '59', '67', '85', '86', '90'}),\n",
       "  frozenset({'23', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '59', '76', '85', '86', '90'}),\n",
       "  frozenset({'34', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '59', '63', '67', '85', '86'}),\n",
       "  frozenset({'34', '63', '67', '85', '86', '90'}),\n",
       "  frozenset({'23', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '63', '76', '85', '86', '90'}),\n",
       "  frozenset({'34', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'36', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '67', '76', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '59', '85', '90', '93'})],\n",
       " [frozenset({'1', '110', '24', '36', '85', '86', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '36', '85', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '36', '86', '90'}),\n",
       "  frozenset({'1', '110', '24', '34', '36', '85', '86'}),\n",
       "  frozenset({'1', '110', '24', '34', '85', '86', '90'}),\n",
       "  frozenset({'1', '24', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'110', '34', '36', '53', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '56', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '53', '63', '85', '86', '90'}),\n",
       "  frozenset({'110', '24', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'1', '110', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'24', '34', '53', '85', '86', '90', '94'}),\n",
       "  frozenset({'34', '53', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'28', '34', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '85', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '28', '34', '39', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'34', '39', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'34', '39', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '63', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'34', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '63', '86'}),\n",
       "  frozenset({'23', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'36', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '86'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'34', '36', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '85', '86'}),\n",
       "  frozenset({'36', '39', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '63'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '63', '85'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '85', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '63', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '63', '85', '86'}),\n",
       "  frozenset({'2', '34', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '86', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '85', '86', '90'}),\n",
       "  frozenset({'2', '34', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '85', '86'}),\n",
       "  frozenset({'2', '34', '36', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '85', '86', '93'}),\n",
       "  frozenset({'2', '36', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'2', '36', '39', '59', '63', '85', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '85', '93'}),\n",
       "  frozenset({'2', '36', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '85', '93'}),\n",
       "  frozenset({'36', '59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'34', '36', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '36', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '85', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '90'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '90', '93'})],\n",
       " [frozenset({'1', '110', '24', '34', '36', '85', '86', '90'}),\n",
       "  frozenset({'2', '28', '34', '39', '53', '85', '86', '90'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '63', '85'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '86', '93'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '63', '85', '86'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '63', '86'}),\n",
       "  frozenset({'2', '34', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '86', '90'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '86', '90', '93'}),\n",
       "  frozenset({'34', '36', '59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '34', '59', '63', '85', '86', '90', '93'}),\n",
       "  frozenset({'23', '36', '59', '63', '85', '86', '90', '93'})],\n",
       " [frozenset({'2', '23', '34', '36', '39', '59', '63', '85', '86'}),\n",
       "  frozenset({'23', '34', '36', '39', '59', '85', '86', '90', '93'}),\n",
       "  frozenset({'2', '23', '34', '36', '39', '59', '85', '86', '93'}),\n",
       "  frozenset({'23', '34', '36', '59', '63', '85', '86', '90', '93'})],\n",
       " []]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "frozenset({'2', '28'})\n",
      "frozenset({'2', '53'})\n",
      "frozenset({'2', '23'})\n",
      "frozenset({'2', '34'})\n",
      "frozenset({'2', '36'})\n",
      "frozenset({'2', '59'})\n",
      "frozenset({'2', '63'})\n",
      "frozenset({'2', '67'})\n",
      "frozenset({'2', '76'})\n",
      "frozenset({'2', '85'})\n",
      "frozenset({'2', '86'})\n",
      "frozenset({'2', '90'})\n",
      "frozenset({'2', '93'})\n",
      "frozenset({'2', '39'})\n"
     ]
    }
   ],
   "source": [
    "# 在结果中搜索含有毒特征值为2的频繁项集：\n",
    "for item in L[1]:\n",
    "    if '2' in item :\n",
    "        print(item)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "frozenset({'2', '28', '34', '85'})\n",
      "frozenset({'59', '2', '28', '34'})\n",
      "frozenset({'59', '2', '63', '28'})\n",
      "frozenset({'59', '2', '28', '85'})\n",
      "frozenset({'59', '2', '28', '90'})\n",
      "frozenset({'59', '39', '2', '28'})\n",
      "frozenset({'63', '2', '28', '34'})\n",
      "frozenset({'63', '2', '28', '85'})\n",
      "frozenset({'86', '53', '2', '28'})\n",
      "frozenset({'86', '39', '2', '28'})\n",
      "frozenset({'86', '2', '28', '34'})\n",
      "frozenset({'86', '59', '2', '28'})\n",
      "frozenset({'86', '63', '2', '28'})\n",
      "frozenset({'86', '2', '28', '85'})\n",
      "frozenset({'86', '2', '28', '90'})\n",
      "frozenset({'2', '28', '90', '34'})\n",
      "frozenset({'2', '28', '90', '85'})\n",
      "frozenset({'39', '2', '28', '90'})\n",
      "frozenset({'53', '2', '28', '90'})\n",
      "frozenset({'39', '2', '28', '34'})\n",
      "frozenset({'39', '2', '63', '28'})\n",
      "frozenset({'39', '2', '28', '85'})\n",
      "frozenset({'53', '2', '28', '34'})\n",
      "frozenset({'53', '2', '28', '85'})\n",
      "frozenset({'39', '53', '2', '28'})\n",
      "frozenset({'53', '2', '34', '85'})\n",
      "frozenset({'53', '39', '2', '34'})\n",
      "frozenset({'86', '53', '39', '2'})\n",
      "frozenset({'86', '53', '2', '34'})\n",
      "frozenset({'86', '53', '2', '85'})\n",
      "frozenset({'86', '53', '2', '90'})\n",
      "frozenset({'53', '39', '2', '90'})\n",
      "frozenset({'53', '2', '90', '34'})\n",
      "frozenset({'53', '2', '90', '85'})\n",
      "frozenset({'53', '2', '39', '85'})\n",
      "frozenset({'23', '2', '34', '85'})\n",
      "frozenset({'23', '2', '34', '93'})\n",
      "frozenset({'23', '2', '85', '93'})\n",
      "frozenset({'23', '2', '36', '34'})\n",
      "frozenset({'59', '23', '2', '36'})\n",
      "frozenset({'23', '2', '36', '85'})\n",
      "frozenset({'23', '2', '36', '93'})\n",
      "frozenset({'39', '2', '36', '34'})\n",
      "frozenset({'59', '2', '39', '36'})\n",
      "frozenset({'59', '2', '36', '34'})\n",
      "frozenset({'39', '2', '36', '85'})\n",
      "frozenset({'2', '36', '34', '85'})\n",
      "frozenset({'59', '2', '36', '85'})\n",
      "frozenset({'36', '2', '90', '34'})\n",
      "frozenset({'36', '2', '90', '85'})\n",
      "frozenset({'36', '2', '90', '93'})\n",
      "frozenset({'39', '2', '36', '93'})\n",
      "frozenset({'2', '36', '34', '93'})\n",
      "frozenset({'59', '2', '36', '93'})\n",
      "frozenset({'2', '36', '85', '93'})\n",
      "frozenset({'59', '23', '2', '34'})\n",
      "frozenset({'59', '23', '2', '85'})\n",
      "frozenset({'59', '23', '2', '93'})\n",
      "frozenset({'59', '2', '34', '85'})\n",
      "frozenset({'59', '2', '34', '93'})\n",
      "frozenset({'59', '2', '85', '93'})\n",
      "frozenset({'23', '2', '63', '34'})\n",
      "frozenset({'23', '2', '63', '85'})\n",
      "frozenset({'2', '23', '63', '36'})\n",
      "frozenset({'2', '63', '36', '34'})\n",
      "frozenset({'59', '2', '63', '36'})\n",
      "frozenset({'2', '63', '36', '85'})\n",
      "frozenset({'2', '63', '36', '90'})\n",
      "frozenset({'2', '63', '36', '93'})\n",
      "frozenset({'59', '2', '23', '63'})\n",
      "frozenset({'59', '2', '63', '34'})\n",
      "frozenset({'59', '2', '63', '85'})\n",
      "frozenset({'59', '2', '63', '90'})\n",
      "frozenset({'59', '2', '63', '93'})\n",
      "frozenset({'2', '63', '34', '85'})\n",
      "frozenset({'2', '63', '90', '34'})\n",
      "frozenset({'2', '63', '90', '85'})\n",
      "frozenset({'2', '63', '90', '93'})\n",
      "frozenset({'2', '63', '34', '93'})\n",
      "frozenset({'2', '63', '85', '93'})\n",
      "frozenset({'67', '2', '34', '85'})\n",
      "frozenset({'2', '76', '34', '85'})\n",
      "frozenset({'2', '34', '85', '93'})\n",
      "frozenset({'86', '23', '2', '34'})\n",
      "frozenset({'86', '23', '2', '85'})\n",
      "frozenset({'86', '23', '2', '93'})\n",
      "frozenset({'86', '2', '23', '36'})\n",
      "frozenset({'86', '2', '36', '34'})\n",
      "frozenset({'86', '59', '2', '36'})\n",
      "frozenset({'86', '2', '36', '85'})\n",
      "frozenset({'86', '2', '36', '93'})\n",
      "frozenset({'86', '59', '2', '23'})\n",
      "frozenset({'86', '59', '2', '34'})\n",
      "frozenset({'86', '59', '2', '85'})\n",
      "frozenset({'86', '59', '2', '93'})\n",
      "frozenset({'86', '2', '23', '63'})\n",
      "frozenset({'86', '2', '63', '34'})\n",
      "frozenset({'86', '2', '63', '36'})\n",
      "frozenset({'86', '59', '2', '63'})\n",
      "frozenset({'86', '2', '63', '85'})\n",
      "frozenset({'86', '2', '63', '90'})\n",
      "frozenset({'86', '2', '63', '93'})\n",
      "frozenset({'86', '67', '2', '34'})\n",
      "frozenset({'86', '2', '34', '76'})\n",
      "frozenset({'86', '2', '34', '85'})\n",
      "frozenset({'86', '67', '2', '85'})\n",
      "frozenset({'86', '2', '76', '85'})\n",
      "frozenset({'86', '2', '23', '90'})\n",
      "frozenset({'86', '2', '90', '34'})\n",
      "frozenset({'86', '36', '2', '90'})\n",
      "frozenset({'86', '59', '2', '90'})\n",
      "frozenset({'86', '2', '90', '85'})\n",
      "frozenset({'86', '2', '90', '93'})\n",
      "frozenset({'86', '2', '34', '93'})\n",
      "frozenset({'86', '2', '85', '93'})\n",
      "frozenset({'23', '2', '90', '34'})\n",
      "frozenset({'59', '23', '2', '90'})\n",
      "frozenset({'23', '2', '90', '85'})\n",
      "frozenset({'23', '2', '90', '93'})\n",
      "frozenset({'39', '2', '90', '34'})\n",
      "frozenset({'59', '2', '39', '90'})\n",
      "frozenset({'59', '2', '90', '34'})\n",
      "frozenset({'39', '2', '90', '85'})\n",
      "frozenset({'2', '90', '34', '85'})\n",
      "frozenset({'59', '2', '90', '85'})\n",
      "frozenset({'39', '2', '90', '93'})\n",
      "frozenset({'2', '90', '34', '93'})\n",
      "frozenset({'59', '2', '90', '93'})\n",
      "frozenset({'2', '90', '85', '93'})\n",
      "frozenset({'39', '23', '2', '34'})\n",
      "frozenset({'39', '23', '2', '59'})\n",
      "frozenset({'39', '23', '2', '85'})\n",
      "frozenset({'39', '23', '2', '93'})\n",
      "frozenset({'39', '2', '59', '34'})\n",
      "frozenset({'39', '2', '34', '76'})\n",
      "frozenset({'39', '2', '34', '85'})\n",
      "frozenset({'39', '2', '34', '93'})\n",
      "frozenset({'39', '23', '2', '63'})\n",
      "frozenset({'39', '2', '63', '34'})\n",
      "frozenset({'39', '2', '63', '36'})\n",
      "frozenset({'39', '59', '2', '63'})\n",
      "frozenset({'39', '2', '63', '85'})\n",
      "frozenset({'39', '2', '63', '90'})\n",
      "frozenset({'39', '2', '63', '93'})\n",
      "frozenset({'67', '39', '2', '34'})\n",
      "frozenset({'67', '39', '2', '85'})\n",
      "frozenset({'39', '2', '59', '85'})\n",
      "frozenset({'39', '2', '76', '85'})\n",
      "frozenset({'86', '39', '23', '2'})\n",
      "frozenset({'86', '39', '2', '34'})\n",
      "frozenset({'86', '39', '2', '36'})\n",
      "frozenset({'86', '39', '59', '2'})\n",
      "frozenset({'86', '39', '2', '63'})\n",
      "frozenset({'86', '67', '39', '2'})\n",
      "frozenset({'86', '39', '2', '76'})\n",
      "frozenset({'86', '39', '2', '85'})\n",
      "frozenset({'86', '39', '2', '90'})\n",
      "frozenset({'86', '39', '2', '93'})\n",
      "frozenset({'39', '2', '59', '93'})\n",
      "frozenset({'39', '2', '85', '93'})\n"
     ]
    }
   ],
   "source": [
    "for item in L[3]:\n",
    "    if '2' in item :\n",
    "        print(item)"
   ]
  }
 ],
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